FIN 3113 Chapter 5 HW

What's the interest rate of a 5-year, annual $5,300 annuity with present value of $21,500? (Use a time value of money calculator or a spreadsheet. Round your answer to 2 decimal places.)

$21,500 =$5,300×(1−1/(1+i)^5 All divided by i ⇒ i = 7.40% Or N = 5, PV = −21,500, PMT = 5,300, FV = 0, CPT I = 7.400

Payday loans are very short-term loans that charge very high interest rates. You can borrow $200 today and repay $280 in two weeks. What is the compounded annual rate implied by this 40 percent rate charged for only two weeks? (Hint: Compound the 2-week return 26 times for the annual return.) (Do not round intermediate calculations and round your final answer to the nearest whole percent.)

40 percent for two weeks needs to be compounded 26 times to form a year: (1 + i)^26 - 1 = (1 + 0.40)^26 - 1 = 6,298.83 = 629,883%. Note: Use the unrounded percent of increase in the computation.

Assume that you contribute $340 per month to a retirement plan for 25 years. Then you are able to increase the contribution to $680 per month for another 25 years. Given a 9.0 percent interest rate, what is the value of your retirement plan after the 50 years? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Break the annuity streams into a level stream of payments of $340 for 50 years and another level stream of payments of $340 for the last 25 years. FVA50+FVA25 =$340×(1+0.090/12)^600−1 Divided by 0.090/12 + $340×(1+0.090/12)^300−1 Divided by 0.090/12 =$340×11,669.1019+$340×1,121.1219 =$4,348,676.09 Or N = 50 × 12, I = 9.0/12, PV = 0, PMT = −340, CPT FV == 3,967,494.63 and N = 25 × 12, I = 9.0/12, PV = 0, PMT = −340, CPT FV == 381,181.46 Sum the FVs to get $4,348,676.09.

A loan is offered with monthly payments and a 8.25 percent APR. What's the loan's effective annual rate (EAR)? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

EAR=[1+(0.0825/12)]^12 − 1 =0.0857 =8.57%

Given a 3 percent interest rate, compute the year 6 future value of deposits made in years 1, 2, 3, and 4 of $1,800, $2,100, $2,100, and $2,200, respectively. (Do not round intermediate calculations and round your final answer to 2 decimal places.)

FV6 = $1,800 × (1 + 0.03)^5 + $2,100 × (1 + 0.03)^4 + $2,100 × (1 + 0.03)^3 + $2,200 × (1 + 0.03)^2 FV6 = $2,086.69 + $2,363.57 + $2,294.73 + $2,333.98 = $9,078.97.

Compute the future value in year 8 of a $2,300 deposit in year 1, and another $1,800 deposit at the end of year 3 using a 10 percent interest rate. (Do not round intermediate calculations and round your final answer to 2 decimal places.)

FV8 = $2,300 × (1 + 0.10)^7 + $1,800 × (1 + 0.10)^5 = $4,482.05 + $2,898.92 = $7,380.97. Or N = 7, I = 10, PV = −2,300, PMT = 0, CPT FV == 4,482.05 and N = 5, I = 10, PV = −1,800, PMT = 0, CPT FV == 2,898.92 then $4,482.05 + $2,898.92 = $7,380.97.

What is the future value of a $620 annuity payment over four years if interest rates are 8 percent? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

FVA4 =$620×(1+0.08)^4−1 Divided by 0.08 =$620×4.5061 =$2,793.79 Or N = 4, I = 8, PV = 0, PMT = −620, CPT FV == 2,793.79

If you start making $120 monthly contributions today and continue them for five years, what's their future value if the compounding rate is 9.50 percent APR? (Do not round intermediate calculations and round your final answer to 2 decimal places.) What is the present value of this annuity? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

FVA60=$120×(1+0.0950/12)^60 - 1 Divided by 0.0950/12 ×(1+0.0950/12) =$120×76.422249×1.007917 =$9,243.27 PVA60=$120×[1−(1/(1+0.0950/12)^60 Divided by 0.0950/12]×1.007917 =$120×47.614827×1.007917 =$5,759.01 Or N = 5 × 12, I = 9.50/12, PV = 0, PMT = −120, CPT FV == 9,243.27 use DUE or BGN setting. and N = 5 × 12, I = 9.50/12, PMT = −120, FV = 0, CPT PV == 5,759.01 use DUE or BGN setting.

Given a 5 percent interest rate, compute the present value of payments made in years 1, 2, 3, and 4 of $1,100, $1,300, $1,300, and $1,600, respectively. (Do not round intermediate calculations and round your final answer to 2 decimal places.)

PV = $1,100 ÷ (1 + 0.05)^1 + $1,300 ÷ (1 + 0.05)^2 + $1,300 ÷ (1 + 0.05)^3 + $1,600 ÷ (1 + 0.05)^4 PV = $1,047.62 + $1,179.14 + $1,122.99 + $1,316.32 = $4,666.07 Or N = 1, I = 5, PMT = 0, FV = −1,100, CPT PV == 1,047.62 and N = 2, I = 5, PMT = 0, FV = −1,300, CPT PV == 1,179.14 and N = 3, I = 5, PMT = 0, FV = −1,300, CPT PV == 1,122.99 and N = 4, I = 5, PMT = 0, FV = −1,600, CPT PV == 1,316.32

Compute the present value of a $2,600 deposit in year 1, and another $2,100 deposit at the end of year 3 if interest rates are 10 percent. (Do not round intermediate calculations and round your final answer to 2 decimal places.)

PV = $2,600 ÷ (1 + 0.10)^1 + $2,100 ÷ (1 + 0.10)^3 = $2,363.64 + $1,577.76 = $3,941.40. Or N = 1, I = 10, PMT = 0, FV = −2,600, CPT PV == 2,363.64 and N = 3, I = 10, PV = −2,100, PMT = 0, CPT FV == 1,577.76 then $2,363.64 + $1,577.76 = $3,941.40.

What's the present value, when interest rates are 7.5 percent, of a $80 payment made every year forever? (Round your answer to 2 decimal places.)

PV of a perpetuity =$80/0.075 =$1,066.67

What's the present value of a $840 annuity payment over four years if interest rates are 8 percent? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

PVA4 =$840×[1−1/(1+0.08)^4 Divided By 0.08] =$840×3.312127 =$2,782.19 Or N = 4, I = 8, PMT = −840, FV = 0, CPT PV == 2,782.19

You are looking to buy a car. You can afford $690 in monthly payments for five years. In addition to the loan, you can make a $790 down payment. If interest rates are 9.00 percent APR, what price of car can you afford (loan plus down payment)? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

PVA60 =$690×[1−1(1+0.0900/12)^60 Divided by 0.0900/12]+$790 =$33,239.63+$790 =$34,029.63 Or N = 5 × 12, I = 9.00/12, PMT = −690, FV = 0, CPT PV == 33,239.63 Add the down payment of $790 to get $34,029.63.

If the present value of an ordinary, 8-year annuity is $7,000 and interest rates are 8.0 percent, what's the present value of the same annuity due? (Round your answer to 2 decimal places.)

PVA8 due = $7,000 × (1 + 0.080) = $7,560.00.

Monica has decided that she wants to build enough retirement wealth that, if invested at 10 percent per year, will provide her with $5,500 of monthly income for 25 years. To date, she has saved nothing, but she still has 30 years until she retires. How much money does she need to contribute per month to reach her goal? First compute how much money she will need at retirement, then compute the monthly contribution to reach that goal. (Do not round intermediate calculations and round your final answer to 2 decimal places.)

PVA⁢= $5,500 ×[ 1 − 1 (1 +0.10 /12 )^300 All divided by 0.10 /12 ] ⁢=$605,259.77 Or N = 25 × 12, I = 10/12, PMT = −5,500, FV = 0, CPT PV = 605,259.77 This amount will become the future value in the next calculation, assuming 10 percent interest and 360 level monthly payments. $605,259.77 ⁢=PMT× (1 +0.10 /12 )^360 −1 Divided by 0.10 /12 ⇒PMT=$267.76 Or N = 30 × 12, I = 10/12, PV = 0, FV = 605,259.77, CPT PMT = −267.76