Question

6) Sharon Marsh just graduated. She plans to work for five years and then leave for the Australian "Outback" Country for an extended vacation. She figures she can save $3,500 at the end of each of the first three years and $5,000 at the end of each of two years after. Her family also gave her a graduation gift today of $2,500. Sharon sets up a savings account that offers her an APR of 7.75% which compounds annually. What is her bank account worth at the end of the fifth year before she heads to Australia? (try using the NFV on the calculator)

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7) You have just retired with savings of $ 1.5 million. If you expect to live for 30 years and earn 8% a year on your savings, how much can you afford to spend each year? Assume that the spending occurs at the beginning of the year. (Don't forget about BGN mode)

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8) Lottery prizes are often not "worth" as much as claimed. What is the present value of a prize of $5,000,000 that is to be received in 20 equal yearly instalments, with the first payment beginning today? Assume an interest rate of 7%

(The equal yearly payments will be equal to 5,000,000/20, in case the question was not clear. Also don't forget BGN mode)

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9) Miller's Hardware plans on saving $42,000, $54,000 and $58,000 at the end of each year for the next three years, respectively. How much will the firm have saved at the end of the three years if it can earn 4.5% on its savings?

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10) A sum of $3,000 is deposited into an account paying 10% annually. If $1,206 is withdrawn at the end of years 1 and 2, how much remains in the account at the end of year 2?

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Answer 1

Answer to Q#6 (First question in the list): As gift amount was given by family today itself, it will earn interest for next 5 years. However, remaining deposits occur at the end of each year only. As the deposits are made at the end of each year, amount deposited at the end of year-1 will earn interest for next 4 years; year-2's deposit will earn interest for next 3 years; year-3's deposit will earn interest for next 2 years; year-4's deposit will earn interest for next 1 year; year-5's deposit will earn interest for year. # of periods of deposit to maturity Future value of a lumpsum deposit = Initial amount of deposit x (1 + Periodic interest rate) Year-3 Year-o $2,500 7.75% 5 $3,631.00 Year-1 Year-2 $3,500 $3,500 7.75% 7.75% 4 3 $4,717.77 $4,378.44 $3,500 7.75% Year-4 $5,000 7.75% Amount deposited at the end of year Interest rate per year # of years left to maturity Future value at the end of 5 years Year-5 $5,000 7.75% 2 1 0 $4,063.52 $5,387.50 $5,000.00 Therefore, accumulated future value in the account at the end of 5 years $27,178.24 [$3631.00 + $4717.77 + $4378.44 + $4063.52 + $5387.50 + $5000.00] NOTE: Year-O deposit's future value = $2500 X (1+7.75%)^5 = $2500 x 1.077545 = $2500 x 1.4524 = $3631.00; Year-1 deposit's future value = $3500 x (1+7.75%)^4 = $3500 x 1.0775^4 = $3500 x 1.34794 = $4717.77; Year-2 deposit's future value = $3500 X (1+7.75%)^3 = $3500 x 1.0775^3 = $3500 x 1.25098 = $4378.44; Year-3 deposit's future value = $3500 x (1+7.75%)^2 = $3500 x 1.0775^2 = $3500 x 1.16101 = $4063.52; Year-4 deposit's future value = $5000 X (1+7.75%)^1 = $5000 x 1.077541 = $5000 x 1.0775 = $5387.5; Year-5 deposit's future value = $5000 X (1+7.75%)^0 = $5000 x 1.0775^0 = $5000 x 1 = $5000.