chapter 5-6

If you borrow $200,000 for thirty years to buy a house at an interest rate of 6.0% per year, what is the monthly loan payment?

$1,199.10

Assume that you will invest $200 in one year, $400 in two years, and $600 in three years. If you earn an interest rate of 7.2% per year, how much will you have in three years?

$1,258.64 Future value = 200(1.0722) + 400(1.072) + 600 = 1,258.64

Assume that you borrow $200,000 for five years at an interest rate of 7.9% per year. If the loan has monthly payments, what is the amount of interest in the first payment?

$1,316.67 First payment interest = 200,000(0.079/12) = 1,316.67

What is the present value of an ordinary annuity that pays $200 annually for nine years if the discount rate is 5.6% per year?

$1,384.34 PMT = 200, N = 9, I = 5.6, FV = 0, CPT PV = 1,384.34

What is the present value of an ordinary annuity that pays $300 every six months for four years if the discount rate is 5.6% per year?

$2,098.25 PMT = 300, N = 4x2 = 8, I = 5.6/2 = 2.8, FV = 0, CPT PV = 2,123.79

Assume that you borrow $40,000 for three years at an interest rate of 5.2% per year. If the loan has quarterly payments, what is the amount of principal in the first payment?

$3,101.67 PV = 40,000, N = 3x4 = 12, I = 5.2/4 = 1.3, FV = 0, CPT PMT = 3,621.67 First payment interest = 40,000(0.0013) = 520.00 First payment principal = 3,621.67 - 520.00 = 3,101.67

Assume that you borrow $15,500 for four years at an interest rate of 9.2% per year. If the loan has annual payments, what is the amount of principal in the first payment?

$3,379.38 PV = 15,500, N = 4, I = 9.2, FV = 0, CPT PMT = 4,805.38 First payment interest = 15,500(0.092) = 1,426.00 First payment principal = 4,805.38 - 1,426.00 = 3,379.38

What is the future value of an ordinary annuity that pays $700 every six months for three years if the interest rate is 8.4% per year?

$4,666.49 PMT = 700, N = 3x2 = 6, I = 8.4/2 = 4.2, PV = 0, CPT FV = 4,666.49

Assume that you borrow $24,000 for four years at an interest rate of 8.0% per year. If the loan has annual payments, what is the total amount of interest that you will pay over the life of the loan?

$4,984.40 PV = 24,000, N = 4, I = 8.0, FV = 0, CPT PMT = 7,246.10 Total payments = 7,246.10(4) = 28,984.40 Total interest paid = 28,984.40 - 24,000 = 4,984.40

If you borrow $36,000 for five years to buy a car at an interest rate of 5.9% per year, what is the monthly loan payment?

$694.31 PV = 36,000, N = 5x12 = 60, I = 5.9/12 = 0.492, FV = 0, CPT PMT = 694.31

If the present value of a perpetuity is $122,138.90 when the discount rate is 7.3% per year, what is the amount of the annual payment?

$8,916.14 Payment = 122,138.90(0.073) = 8,916.14

Assume that you invest $500 today and you earn a return of 6.6% per year, compounded monthly. How much will you have after ten years?

$965.65 PV = 500, N = 10x12 = 120, I = 6.6/12 = 0.55, PMT = 0, CPT FV = 965.65

Twelve-year Treasury bonds are yielding 5.8% per year and a twelve-year corporate bond is yielding 7.4% per year. If the corporate bond's yield includes a 0.8% per year default premium and a 2.1% per year inflation premium, what is its liquidity premium?

.8% Liquidity premium = 7.4 - 5.8 - 0.8 = 0.8

If the present value of a perpetuity is $12,638.50 when the discount rate is 9.3% per year, what is the amount of the annual payment?

1,175.38 Payment = 12,638.50(0.093) = 1,175.38

What is the future value of $670 in six years if the interest rate is 11.3% per year?

1,273.64 PV = 670, N = 6, I = 11.3, PMT = 0, CPT FV = 1,273.64

Assume that you will invest $300 in one year, $400 in two years, and $500 in three years. If you earn an interest rate of 8.2% per year, how much will you have in three years?

1,284.02 Future value = 300(1.0822) + 400(1.082) + 500 = 1,284.02

You currently have $600 in a bank account. Assume that you will deposit $100 in one year, $200 in two years, and $300 in three years. If you earn an interest rate of 5.1% per year, how much will you have in three years?

1,317.22 Future value = 600(1.0513) + 100(1.0512) + 200(1.051) + 300 = 1,317.22

What is the present value of an ordinary annuity that pays $500 annually for four years if the discount rate is 11.3% per year?

1,541,34 PMT = 500, N = 4, I = 11.3, FV = 0, CPT PV = 1,541,34

If you borrow $225,000 for fifteen years to buy a house at an interest rate of 3.6% per year, what is the monthly loan payment?

1,619.56 PV = 225,000, N = 15x12 = 180, I = 3.6/12 = 0.3, FV = 0, CPT PMT = 1,619.56

Ten-year Treasury bonds are yielding 6.4% per year and a ten-year corporate bond is yielding 8.1% per year. If the corporate bond's yield includes a 0.4% per year liquidity premium, what is its default premium?

1.3% Default premium = 8.1 - 6.4 - 0.4 = 1.3

The risk-free interest rate is 4.1% per year, the liquidity premium is 0.5% per year, the maturity premium is 0.7% per year, the inflation premium is 2.2% per year, and the default premium is 2.7% per year. What is the annual real interest rate?

1.9% Real interest rate = 4.1 - 2.2 = 1.9

What annual interest rate is required for an amount to double in seven years?

10.4 PV = -1, FV = 2, N = 7, PMT = 0, CPT I = 10.4

Assume that you borrow $100,000 for five years at an interest rate of 6.0% per year. If the loan has semiannual payments, what is the total amount of interest that you will pay over the life of the loan?

117,230.50 PV = 100,000, N = 5x2 = 10, I = 6.0/2 = 3.0, FV = 0, CPT PMT = 11,723.05 Total payments = 11,723.05(10) = 117,230.50

If the present value of an ordinary annuity that pays $600 each year for seven years is $2,703.87, what is the annual discount rate?

12.4 PV = 2,703.87, PMT = -600, N = 7, FV = 0, CPT I = 12.4

What is the present value of $200 to be received in nine years if the discount rate is 5.7% per year?

121.44 FV = 200, N = 9, I = 5.7, PMT = 0, CPT PV = 121.44

Assume that you will invest $500 in one year, $400 in two years, and $500 in three years. If you earn an interest rate of 5.2% per year, how much will you have in three years?

1474.15 Future value = 500(1.0522) + 400(1.052) + 500 = 1,474.15

What is the present value of a perpetuity that pays $1,250 per year when the discount rate is 8.1% per year?

15,432.10 PV = 1,250/0.081 = 15,432.10

Eight years ago you invested $400 and the investment is now worth $1,359. What annual rate of return did you earn?

16.5 PV = -400, FV = 1,359, N = 8, PMT = 0, CPT I = 16.5

Assume that you have $200,000 in your retirement account, you plan to invest $10,000 at the end of each year, and your goal is to have $800,000. If you earn an interest rate of 5.9% per year, how many years will it take for you to achieve your goal?

16.8 PV = 200,000, PMT = 10,000, FV = -800,000, I = 5.9, CPT N = 16.8

What is the present value of a perpetuity that pays $20,000 per year when the discount rate is 12.1% per year?

165,289.26 PV = 20,000/0.121 = 165,289.26

What is the future value of $75 in ten years if the interest rate is 9.7% per year?

189.29 PV = 75, N = 10, I = 9.7, PMT = 0, CPT FV = 189.29

If you borrow $8,000 for five years at an interest rate of 6.5% per year, what is the annual loan payment?

1925.08 PV = 8,000, N = 5, I = 6.5, FV = 0, CPT PMT = 1,925.08

Assume that you borrow $30,800 for five years at an interest rate of 6.3% per year. If the loan has annual payments, what is the amount of interest in the first payment?

1940.40 First payment interest = 30,800(0.063) = 1,940.40

If the discount rate is 12.4% per year, what is the present value of $450 to be received in seven years?

198.54 FV = 450, N = 7, I = 12.4, PMT = 0, CPT PV = 198.54

What is the future value of an ordinary annuity that pays $175 annually for ten years if the interest rate is 6.6% per year?

2,372.68 PMT = 175, N = 10, I = 6.6, PV = 0, CPT FV = 2,372.68

What annual interest rate is required for an amount to triple in six years?

20.1 PV = -1, FV = 3, N = 6, PMT = 0, CPT I = 20.1

Assume that you have $100,000 in your retirement account, you plan to invest $15,000 at the end of each year, and your goal is to have $1,000,000. If you earn an interest rate of 6.7% per year, how many years will it take for you to achieve your goal?

20.5 V = 100,000, PMT = 15,000, FV = -1,000,000, I = 6.7, CPT N = 20.5

Assume that you borrow $18,000 for five years at an interest rate of 4.8% per year. If the loan has annual payments, what is the amount of principal in the first payment?

3,270.59 PV = 18,000, N = 5, I = 4.8, FV = 0, CPT PMT = 4,134.59 First payment interest = 18,000(0.048) = 864.00 First payment principal = 4,134.59 - 864.00 = 3,270.59

Assume that you borrow $50,000 for ten years at an interest rate of 6.7% per year. If the loan has annual payments, what is the amount of principal in the first payment?

3,670.48 PV = 50,000, N = 10, I = 6.7, FV = 0, CPT PMT = 7,020.48 First payment interest = 50,000(0.067) = 3,350.00 First payment principal = 7,020.48 - 3,350.00 = 3,670.48

The real interest rate is 2.1% per year, the liquidity premium is 0.4% per year, the maturity premium is 0.7% per year, and the default premium is 2.1% per year. If the risk-free interest rate is 5.4% per year, what is the annual inflation premium?

3.3% Inflation premium = 5.4 - 2.1 = 3.3

If the future value of an ordinary annuity that pays $700.00 each month for six years is $56,163.60, what is the annual interest rate?

3.6 FV = 56,163.60, PMT = -700.00, N = 6x12 = 72, PV = 0, CPT I = 0.3000 Annualize, 0.3000(12) = 3.6

The inflation rate is expected to be 1.8% per year for the next two years and 2.4% per year thereafter. If the real interest rate is 1.7% per year, what is the annual yield on three-year Treasury securities?

3.7% The inflation rate is expected to be 1.8% per year for the next two years and 2.4% per year thereafter. If the real interest rate is 1.7% per year, what is the annual yield on three-year Treasury securities?

If the inflation premium is 1.5% per year, the liquidity premium is 0.2% per year, the maturity premium is 0.5% per year, the real interest rate is 2.5% per year, and the default premium is 3.5% per year, what is the annual risk-free interest rate?

4% Risk-free interest rate = 2.5 + 1.5 = 4.0

If the present value of an ordinary annuity that pays $350 each month for three years is $11,819.12, what is the annual discount rate?

4.2 PV = 11,819.12, PMT = -350, N = 3x12 = 36, FV = 0, CPT I = 0.3500 Annualize, 0.3500(12) = 4.2

If the future value of an ordinary annuity that pays $175.00 each month for five years is $11,750.47, what is the annual interest rate?

4.5 FV = 11,750.47, PMT = -175.00, N = 5x12 = 60, PV = 0, CPT I = 0.3750 Annualize, 0.3750(12) = 4.5

How many years are required for $1,000 to increase to $1,250 if the interest rate is 5.1% per year?

4.5 PV = -1,000, FV = 1,250, I = 5.1, PMT = 0, CPT N = 4.5

The present value of a perpetuity is $9,444.44 and the annual payment is $425. What is the annual discount rate?

4.5% Discount rate = 425/9,444.44 = 0.045

If the present value of an ordinary annuity that pays $175 each year for ten years is $1,357.89, what is the annual discount rate?

4.9 PV = 1,357.89, PMT = -175, N = 10, FV = 0, CPT I = 4.9

Assume that you borrow $150,000 for seven years at an interest rate of 5.5% per year. If the loan has semiannual payments, what is the amount of interest in the first payment?

4125 First payment interest = 150,000(0.055/2) = 4,125.00

What is the future value of an ordinary annuity that pays $380 annually for nine years if the interest rate is 4.8% per year?

4155.74 PMT = 380, N = 9, I = 4.8, PV = 0, CPT FV = 4,155.74

You intend to lease a $55,000 car. The lease term is six years and the financing rate is 6.3% per year. If the value of the car at the end of the lease is expected to be $40,500, what is the monthly lease payment?

454.99 PV = -55,000, FV = 40,500, N = 6x12 = 72, I = 6.3/12 = 0.5250, CPT PMT = 454.99

If the interest rate is 4.6% per year, how many years are required for $2,000 to increase to $2,500?

5 PV = -2,000, FV = 2,500, I = 4.6, PMT = 0, CPT N = 5.0

If the real interest rate is 2.1% per year, the liquidity premium is 0.7% per year, the maturity premium is 0.9% per year, the inflation premium is 2.9% per year, and the default premium is 3.3% per year, what is the annual risk-free interest rate?

5 Risk-free interest rate = 2.1 + 2.9 = 5.0

Assume that you borrow $75,000 for six years at an interest rate of 4.8% per year. If the loan has semiannual payments, what is the amount of principal in the first payment?

5,467.34 PV = 75,000, N = 6x2 = 12, I = 4.8/2 = 2.4, FV = 0, CPT PMT = 7,267.34 First payment interest = 75,000(0.0024) = 1,800.00 First payment principal = 7,267.34 - 1,800.00 = 5,467.34

You intend to lease a $32,700 car. The lease term is four years and the value of the car at the end of the lease is expected to be $25,200. If the monthly lease payment is $280.16, what is the annual lease financing rate?

5.1% PV = -32,700, FV = 25,200, PMT = 280.16, N = 4x12 = 48, CPT I = 0.4250 Annualize 0.4250(12) = 5.1

If the future value of an ordinary annuity that pays $350 each year for five years is $1,949.48, what is the annual interest rate?

5.4 FV = 1,949.48, PMT = -350, N = 5, PV = 0, CPT I = 5.4

You intend to lease a $45,000 car. The lease term is six years and the value of the car at the end of the lease is expected to be $30,500. If the monthly lease payment is $373.47, what is the annual lease financing rate?

5.4 PV = -45,000, FV = 30,500, PMT = 373.47, N = 6x12 = 72, CPT I = 0.45 Annualize 0.45(12) = 5.4

For an amount to double in twelve years, what annual interest rate is required?

5.9 PV = -10, FV = 20, N = 12, PMT = 0, CPT I = 5.9

If the present value of a perpetuity is $10,638.30 when the discount rate is 4.7% per year, what is the amount of the annual payment?

500 Payment = 10,638.30(0.047) = 500.00

A security will pay $100 in one year, $200 in two years, and $300 in three years. If the appropriate discount rate is 6.7% per year, what is the value of the security today?

516.35 Present value = 100/1.067 + 200/1.0672 + 300/1.0673 = 516.35

If you borrow $32,000 for six years to buy a car at an interest rate of 5.4% per year, what is the monthly loan payment?

521.32 PV = 32,000, N = 6x12 = 72, I = 5.4/12 = 0.450, FV = 0, CPT PMT = 521.32

You intend to lease a $36,000 car. The lease term is four years and the financing rate is 5.3% per year. If the value of the car at the end of the lease is expected to be $16,500, what is the monthly lease payment?

524.60 PV = -36,000, FV = 16,500, N = 4x12 = 48, I = 5.3/12 = 0.4417, CPT PMT = 524.60

What is the present value of $820 to be received in five years if the discount rate is 8.9% per year?

535.40 FV = 820, N = 5, I = 8.9, PMT = 0, CPT PV = 535.40

Assume that you borrow $12,000 for four years at an interest rate of 5.7% per year. If the loan has monthly payments, what is the amount of interest in the first payment?

57 First payment interest = 12,000(0.057/12) = 57.00

Assume that you borrow $4,000 for six years at an interest rate of 5.2% per year. If the loan has annual payments, what is the amount of principal in the first payment?

585.12 PV = 4,000, N = 6, I = 5.2, FV = 0, CPT PMT = 793.12 First payment interest = 4,000(0.052) = 208.00 First payment principal = 793.12 - 208.00 = 585.12

The present value of a perpetuity is $12,500.00 and the annual payment is $750. What is the annual discount rate?

6 Discount rate = 750/12,500 = 0.06

What is the future value of an ordinary annuity that pays $600 annually for eight years if the interest rate is 8.3% per year?

6,451.55 PMT = 600, N = 8, I = 8.3, PV = 0, CPT FV = 6,451.55

Assume that you have $300,000 in your retirement account, you plan to invest $10,000 at the end of each year, and your goal is to have $1,000,000. If you want to retire in 15 years, what annual rate of return must you earn?

6.4 PV = 300,000, PMT = 10,000, FV = -1,000,000, N = 15, CPT I = 6.4

What annual interest rate is required for $365 to increase to $573 in seven years?

6.7 PV = -365, FV = 573, N = 7, PMT = 0, CPT I = 6.7

If the interest rate is 5.4% per year, what is the future value of $400 in eight years?

609.24 PV = 400, N = 8, I = 5.4, PMT = 0, CPT FV = 609.24

If you borrow $25,000 for four years to buy a boat at an interest rate of 8.0% per year, what is the monthly loan payment?

610.32 PV = 25,000, N = 4x12 = 48, I = 8.0/12 = 0.667, FV = 0, CPT PMT = 610.32

Assume that you will invest $100 in one year, $200 in two years, and $300 in three years. If you earn an interest rate of 6.7% per year, how much will you have in three years?

627.25 Future value = 100(1.0672) + 200(1.067) + 300 = 627.25

If you borrow $1,800 for three years at an interest rate of 3.7% per year, what is the annual loan payment?

644.94 PV = 1,800, N = 3, I = 3.7, FV = 0, CPT PMT = 644.94

If you borrow $35,000 for five years to buy a car at an interest rate of 6.0% per year, what is the monthly loan payment?

676.55 PV = 35,000, N = 5x12 = 60, I = 6.0/12 = 0.5, FV = 0, CPT PMT = 676.65

Assume that you have $100,000 in your retirement account, you plan to invest $15,000 at the end of each year, and your goal is to have $1,000,000. If you want to retire in 20 years, what annual rate of return must you earn?

7 PV = 100,000, PMT = 15,000, FV = -1,000,000, N = 20, CPT I = 7.0

If the future value of an ordinary annuity that pays $1,783.96 each year for ten years is $25,000.00, what is the annual interest rate?

7.3 FV = 25,000, PMT = -1,783.96, N = 10, PV = 0, CPT I = 7.3

The present value of a perpetuity is $4,593.10 and the annual payment is $335.30. What is the annual discount rate?

7.3 Discount rate = 335.30/4,593.10 = 0.073

What is the present value of an ordinary annuity that pays $150 annually for seven years if the discount rate is 9.2% per year?

749.90 PMT = 150, N = 7, I = 9.2, FV = 0, CPT PV = 749.90

Assume that you borrow $40,000 for four years at an interest rate of 4.2% per year. If the loan has monthly payments, what is the amount of principal in the first payment?

766.75 PV = 40,000, N = 4x12 = 48, I = 4.2/12 = 0.350, FV = 0, CPT PMT = 906.75 First payment interest = 40,000(0.00350) = 140.00 First payment principal = 906.75 - 140.00 = 766.75

If the discount rate is 13.3% per year, what is the present value of $1,670 to be received in six years?

789.47 FV = 1,670, N = 6, I = 13.3, PMT = 0, CPT PV = 789.47

How many years are required for $845 to increase to $1,770 if the interest rate is 9.1% per year?

8.5 PV = -845, FV = 1,770, I = 9.1, PMT = 0, CPT N = 8.5

If the present value of an ordinary annuity that pays $305 each year for five years is $1,195.64, what is the annual discount rate?

8.7 PV = 1,195.64, PMT = -305, N = 5, FV = 0, CPT I = 8.7

You currently have $200 in a bank account. Assume that you will deposit $300 in one year, $200 in two years, and $100 in three years. If you earn an interest rate of 6.8% per year, how much will you have in three years?

899.42 Future value = 200(1.0683) + 300(1.0682) + 200(1.068) + 100 = 899.42

A five-year Treasury bond is yielding 4.7% per year, which includes a 1.9% per year real rate. If a five-year corporate bond's yield includes a 0.3% per year liquidity premium and a 4.1% per year default premium, what is the yield on the corporate bond?

9.1% Five-year corporate bond yield = 4.7 + 0.3 + 4.1 = 9.1

A security will pay $300 in one year, $300 in two years, and $600 in three years. If the appropriate discount rate is 9.5% per year, what is the value of the security today?

981.17 Present value = 300/1.095 + 300/1.0952 + 600/1.0953 = 981.17

The interest rate on one-year Treasury securities is 3% per year and the interest rate on three-year Treasury securities is 5% per year. What is the approximate expected annual interest rate on two-year Treasury securities one year from now?

Expected annual interest rate on two-year Treasury securities in one year = (3x5 - 3)/2 = 6

The real interest rate is 2.2% per year. If the inflation rate is expected to be 3.0% per year for the next two years and 2.5% per year thereafter, what is the annual yield on five-year Treasury securities?

Five-year Treasury security yield = 2.2 + (3.0 + 3.0 + 2.5 + 2.5 +2.5)/5 = 4.9

The real interest rate is 2.1% per year. If the inflation rate is expected to be 2.2% per year for the next two years and 2.6% per year thereafter, what is the yield on four-year Treasury securities?

Four-year Treasury security yield = 2.1 + (2.2 + 2.2 + 2.6 + 2.6)/4 = 4.5

Assume that you borrow $20,000 for five years at an interest rate of 4.5% per year. If the loan has monthly payments, what is the amount of principal in the first payment?

PV = 20,000, N = 5x12 = 60, I = 4.5/12 = 0.375, FV = 0, CPT PMT = 372.86 First payment interest = 20,000(0.00375) = 75.00 First payment principal = 372.86 - 75.00 = 297.86

Assume that you borrow $230,000 for thirty years to buy a house at an interest rate of 3.9% per year. If the loan has monthly payments, what is the total amount of interest that you will pay over the life of the loan?

PV = 230,000, N = 30x12 = 360, I = 3.9/12 = 0.325, FV = 0, CPT PMT = 1,084.84 Total payments = 1,084.84(360) = 390,542.40 Total interest paid = 390,542.40 - 230,000 = 160,542.40

Assume that you borrow $5,000 for three years at an interest rate of 7.5% per year. If the loan has annual payments, what is the total amount of interest that you will pay over the life of the loan?

PV = 5,000, N = 3, I = 7.5, FV = 0, CPT PMT = 1,922.69 Total payments = 1,922.69(3) = 5,768.06 Total interest paid = 5,768.06 - 5,000 = 768.06

A twelve-year corporate bond's yield includes a 0.7% per year liquidity premium, a 1.1% per year maturity premium, and a 1.2% per year default premium. If the corporate bond is yielding 7.6% per year, what is the yield on a twelve-year Treasury bond?

Twelve-year Treasury bond yield = 7.6 - 0.7 - 1.2 = 5.7

An increase in expected inflation likely will result in ___ interest rates. A decrease in risk likely will result in ___ interest rates.

higher, lower

A decrease in production opportunities likely will result in ___ interest rates. A decrease in expected inflation likely will result in ___ interest rates.

lower, lower