Final Exam Finance

Problem 4-8 Compounding with Different Interest Rates (LG3) A deposit of $750 earns interest rates of 9 percent in the first year and 12 percent in the second year. What would be the second year future value?

FV = PV × (1 + i) (1 + j) FV = $750 × (1 + 0.09) (1 + 0.12) = $750 × 1.09 × 1.12 = $915.60

Problem 5-3 Future Value of an Annuity (LG2) What is the future value of a $900 annuity payment over five years if interest rates are 9 percent?

FVA5 = $900 x (1+0.09)^b -1 /0.09 = $900 x 5.9847 = $5,386.24

Problem 4-29 Solving for Rates (LG7) What annual rate of return is earned on a $1,000 investment when it grows to $2,500 in six years?

FVN = PV × (1 + i)N $2,500 = $1,000 × (1 + i)6 (1 + i)6 = $2,500 / $1,000 (1 + i)6 = 2.5 i = (2.5)(1/6) - 1 = 0.1650 or 16.50%

Problem 5-40 Loan Payments (LG9) You wish to buy a $10,000 dining room set. The furniture store offers you a 3-year loan with an 11 percent APR. What are the monthly payments? How would the payment differ if you paid interest only? What would the consequences of such a decision be?

If you only paid interest over the length of the loan and your principal balance was repaid at the end of the 36 months, your payment would be $91.67 per month (= $10,000 × 0.11 ÷ 12) for interest only and you would owe $10,000 at the end of the 36 months, too.

Problem 4-15 Rule of 72 (LG6) Approximately how many years are needed to double a $100 investment when interest rates are 7 percent per year?

N = 72 / 7 ≈ 10.29 years

Problem 5-7 Present Value of an Annuity (LG4) What's the present value of a $900 annuity payment over five years if interest rates are 9 percent?

PFA5 = $900 x [ 1 - 1/(1 + 0.09)^5 / 0.09 ] = $900 x 3.889651 = $3500.69

Problem 5-5 Present Value (LG3) Compute the present value of a $2,000 deposit in year 1 and another $1,500 deposit at the end of year 3 if interest rates are 10 percent.

PV = $2,000 ÷ (1 + 0.10)1 + $1,500 ÷ (1 + 0.10)3 = $1,818.18 + $1,126.97 = $2,945.15

Problem 5-34 Annuity Interest Rate (LG8) What's the interest rate of a 7-year, annual $4,000 annuity with present value of $20,000?

TVM calculator: N = 7, PV = -20,000, PMT = 4,000, FV = 0, CPT I = 9.20%

Problem 5-41 Number of Annuity Payments (LG9) Joey realizes that he has charged too much on his credit card and has racked up $5,000 in debt. If he can pay $150 each month and the card charges 17 percent APR (compounded monthly), how long will it take him to pay off the debt?

TVM calculator: PV = 5,000, PMT = -150, FV = 0, I = 1.417; CPT N = 45.43 months

Problem 5-15 Effective Annual Rate (LG7) A loan is offered with monthly payments and a 10 percent APR. What's the loan's effective annual rate (EAR)?

EAR = [ 1 + 0.10 / 12 ] ^12 -1 = 0.1047 = 10.47%

roblem 4-36 Solving for Rates (LG7) You invested $3,000 in the stock market one year ago. Today, the investment is valued at $3,750. What return did you earn? What return would you suffer next year for your investment to be valued at the original $3,000?

FVN = PV × (1 + i)N $3,750 = $3,000 × (1 + i)1 (1 + i) = $3,750 / $3,000 i = 1.25 - 1 = 0.25 or 25.00% (first year return is positive) FVN = PV × (1 + i)N $3,000 = $3,750 × (1 + i)1 (1 + i) = $3,000 / $3,750 i = .80 - 1 = - 0.20 or - 20.0% (second year return is negative)

Problem 4-31 Solving for Time (LG8) How many years will it take $2 million to grow to $5 million with an annual interest rate of 7 percent?

FVN = PV × (1 + i)N $5 million = $2 million × (1 + 0.07)N (1.07)N = 5 / 2 (the millions cancel) ln (1.07)N = ln 2.5 N × ln 1.07 = ln 2.5 N = ln 2.5 / ln 1.07 = 0.91629 / 0.06766 = 13.54 years = 13 years, 6.5 months

Problem 4-32 Solving for Time (LG8) How long will it take $2,000 to reach $5,000 when it grows at 10 percent per year?

FVN = PV × (1 + i)N $5,000 = $2,000 × (1 + 0.10)N (1.10)N = 5 / 2 (the thousands cancel) ln (1.10)N = ln 2.5 N × ln 1.10 = ln 2.5 N = ln 2.5 / ln 1.10 = 0.91629 / 0.09531 = 9.61 years = 9 years, 7.4 months

Problem 4-11 Present Value (LG4) What is the present value of a $1,500 payment made in six years when the discount rate is 8 percent?

PV = FV / (1 + i)N PV = $1,500 / (1 + 0.08)6 = $1,500 / 1.58687 = $945.25

Problem 4-12 Present Value (LG4) Compute the present value of an $850 payment made in 10 years when the discount rate is 12 percent.

PV = FV / (1 + i)N PV = $850 / (1 + 0.12)10 = $850 / 3.10585 = $273.68

Problem 4-13 Present Value with Different Discount Rates (LG4) Compute the present value of $1,000 paid in three years using the following discount rates: 6 percent in the first year, 7 percent in the second year, and 8 percent in the third year.

PV = FV / [(1 + i) (1 + j) (1 + k)] PV = $1,000 / [(1 + 0.06) (1 + 0.07) (1 + 0.08)] = $1,000 / [1.06 × 1.07 × 1.08] = $1,000 / 1.22494 = $816.37

Problem 5-27 Present Value of a Perpetuity (LG5) A perpetuity pays $100 per year and interest rates are 7.5 percent. How much would its value change if interest rates increased to 9 percent?

PV of a perpetuity = $100/0.075 = $1,333.33 PV of a perpetuity = $100 / 0.09 = $1,111.11 The difference between these perpetuities is $222.22. The value of the perpetuity decreased with an increase in the interest rate.

Problem 5-10 Present Value of a Perpetuity (LG5) What's the present value, when interest rates are 8.5 percent, of a $75 payment made every year forever? (Round your answer to 2 decimal places.)

PV of a perpetuity = $75 / 0.085 = $882.35

Problem 4-25 Moving Cash Flows (LG5) What is the value in year 3 of a $700 cash flow made in year 6 if interest rates are 10 percent?

PV3 = FV6 / (1 + i)N PV3 = $700 / (1 + 0.10)(6-3) = $700 / 1.3310 = $525.92

Problem 5-12 Present Value of an Annuity Due (LG6) If the present value of an ordinary, 6-year annuity is $8,500 and interest rates are 9.5 percent, what's the present value of the same annuity due?

PVA6 due = $8,500 × (1 + 0.095) = $9,307.50