FINAN 450 CHAP 4
Beatrice invests $1,470 in an account that pays 3 percent simple interest. How much more could she have earned over a 4-year period if the interest had been compounded annually?
Balance Year 4 with simple interest = $1,470 + ($1,470 × 0.03 × 4) = $1,646.40 Balance Year 4 with compound interest = $1,470 × 1.03^4 = $1,654.50 Additional interest = $1,654.50 - $1,646.40 = $8.10
Retirement Investment Advisors, Inc., has just offered you an annual interest rate of 4.8 percent until you retire in 45 years. You believe that interest rates will increase over the next year and you would be offered 5.4 percent per year one year from today. If you plan to deposit $15,000 into the account either this year or next year, how much more will you have when you retire if you wait one year to make your deposit?
FV = $15,000 × 1.048^45 = $123,694.10 FV = $15,000 × 1.054^44 = $151,732.33 Difference = $151,732.33 − 123,694.10 = $28,038.23
Your bank will pay you an interest rate of .167 percent per week. You want to have $29,000 in 7 years. How much will you have to deposit today? Assume 52 weeks per year.
PV = $29,000/1.00167^(7×52) = $15,798.62
You have $11,000 and will invest the money at an interest rate of .33 percent per month until the account is worth $17,200. How many years do you have to wait until you reach your target account value?
$17,200 = $11,000(1.0033)^t t = 135.68 months Years to wait = 135.68/12 = 11.31 years
Rick deposited $3,300 into an account 14 years ago for an emergency fund. Today, that account is worth $5,930. What annual rate of return did Rick earn on this account assuming no other deposits and no withdrawals?
$5,930 = $3,300(1 + r)^14 r = ($5,930/$3,300)^(1/14) − 1 r = .0428, or 4.28%
Jenny needs to borrow $5,500 for four years. The loan will be repaid in one lump sum at the end of the loan term. Which one of the following interest rates is best for Jenny?
6.5 simple interest
You made an investment of $8,000 into an account that paid you an annual interest rate of 3.1 percent for the first 5 years and 7.5 percent for the next 10 years. What was your annual rate of return over the entire 15 years?
FV = $8,000 × 1.031^5 = $9,319.30 FV = $9,319.30 × 1.075^10 = $19,207.37 $19,207.37 = $8,000 × (1 + r)^15 r = ($19,207.37/$8,000)^(1/15) r = .0601, or 6.01%
Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2010, Deutscher-Menzies sold Arkie under the Shower, a painting by renowned Australian painter Brett Whiteley, at auction for a price of $1,100,000. Unfortunately for the previous owner, he had purchased it 3 years earlier at a price of $1,680,000. What was his annual rate of return on this painting?
FV = PV(1 + r)^t Solving for r, we get: r = (FV/PV)^(1/t) - 1 r = ($1,100,000/$1,680,000)^(1/3) - 1 r = -.1317, or -13.17%
An investment offers to triple your money in 24 months (don't believe it). What rate per three months are you being offered?
FV = PV(1 + r)^t Solving for r, we get: r = (FV/PV)^(1/t) - 1 r = ($3/$1)^(1/8) - 1 r = .1472, or 14.72%
You expect to receive $30,000 at graduation in two years. You plan on investing it at 7 percent until you have $125,000. How long will you wait from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
FV = PV(1 + r)^t $125,000 = $30,000(1.07^)t t = ln($125,000/$30,000)/ln 1.07 t = 21.09 years
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)^10 FV = $15,540.50 The difference is: $15,540.50 - 13,430 = $2,110.50
Stacey deposits $5,000 into an account that pays 2 percent interest, compounded annually. At the same time, Kurt deposits $5,000 into an account paying 3.5 percent interest, compounded annually. At the end of three years:
Kurt will have a larger account value than Stacey will
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)^25 PV = $169,140,739.02
a. At 5.3 percent interest, how long does it take to double your money? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. At 5.3 percent interest, how long does it take to quadruple your money? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
a. FV = $2 = $1(1.053)^t t = ln 2/ln 1.053 t = 13.42 years b. FV = $4 = $1(1.053)^t t = ln 4/ln 1.053 t = 26.84 years
You have just made your first $5,000 contribution to your individual retirement account. Assume you earn a 10.2 percent rate of return and make no additional contributions. a. What will your account be worth when you retire in 45 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What if you wait 10 years before contributing? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
a. FV = PV(1 + r)^t FV = $5,000(1.1020)^45 FV = $395,495.69 b. FV = $5,000(1.1020)^35 FV = $149,735.86
Jamie earned $14 in interest on her savings account last year. She has decided to leave the $14 in her account so that she can earn interest on the $14 this year. The interest earned on last year's interest earnings is called:
interest on interest
By definition, a bank that pays simple interest on a savings account will pay interest:
only on the principal amount originally invested