Quiz 2
You have $5,800 to deposit. Regency Bank offers 12 percent per year compounded monthly (1 percent per month), while King Bank offers 12 percent but will only compound annually. How much will your investment be worth in 20 years at each bank?
FV = PV(1 + r)t Regency Bank: FV = $5,800(1.01)^240 FV = $63,176.81 King Bank: FV = $5,800(1.12)^20 FV = $55,948.50
Assume the total cost of a college education will be $235,000 when your child enters college in 18 years. You presently have $53,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child's college education?
FV = PV(1 + r)t Solving for r, we get: r = (FV/PV)1/t - 1r = ($235,000/$53,000)1/18 - 1r = .0863, or 8.63% 8.63%
You're trying to save to buy a new $175,000 Ferrari. You have $35,000 today that can be invested at your bank. The bank pays 2.9 percent annual interest on its accounts. How long will it be before you have enough to buy the car?
FV = PV(1 + r)t Solving for t, we get: t = ln(FV/PV)/ln(1 + r) FV = $175,000 = $35,000(1.029)tt = ln($175,000/$35,000)/ln 1.029t = 56.30 years 56.30 years
compute the future value: Present Value. Years. Interest Rate. 2,960. 7 13 7,846. 16 7 85,381 19 9 221,614 26 5
Future Values: 6,963.71 23,162.68 439,000.18 787,986.85
Suppose you are committed to owning a $175,000 Ferrari. If you believe your mutual fund can achieve an 11.2 percent annual rate of return, and you want to buy the car in 10 years on the day you turn 30, how much must you invest today?
PV = FV/(1 + r)t PV = $175,000/(1.112)10 PV = $60,532.72
Imprudential, Inc., has an unfunded pension liability of $645 million that must be paid in 25 years. To assess the value of the firm's stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 5.5 percent, what is the present value of this liability?
PV = FV/(1 + r)t PV = $645,000,000/(1.055)25PV = $169,140,739.02 $169,140,739.02
First City Bank pays 7 percent simple interest on its savings account balances, whereas Second City Bank pays 7 percent interest compounded annually. If you made a deposit of $7,900 in each bank, how much more money would you earn from your Second City Bank account at the end of 10 years?
The simple interest per year is: $7,900 × .07 = $553 So, after 10 years, you will have: $553 × 10 = $5,530 in interest. The total balance will be $7,900 + 5,530 = $13,430 With compound interest, we use the future value formula: FV = PV(1 +r)t FV = $7,900(1.07)10FV = $15,540.50 The difference is: $15,540.50 - 13,430 = $2,110.50 2,110.50
An investment offers to triple your money in 24 months (don't believe it). What rate per three months are you being offered?
r = (FV/PV)1/t - 1 r = ($3/$1)1/8 - 1 r = .1472, or 14.72%
compute the present value: Future Value. Years Interest rate 19,415 15 7 47,382 8 11 312,176 13 10 629,381 25 13
Present Values: 7,036.89 20,560.31 90,426.27 29,645.07
In 1895, the first U.S. Open Golf Championship was held. The winner's prize money was $150. In 2018, the winner's check was $2,160,000 a.What was the annual percentage increase in the winner's check over this period? b. If the winner's prize increases at the same rate, what will it be in 2048?
a. r = (FV/PV)1/t - 1 r = ($2,160,000/$150)1/123 - 1 r = .0810, or 8.10% b. FV = PV(1 + r)t FV = $2,160,000(1.0810)30 FV = $22,319,707.83
