Question

When you were born your parents set up a bank account in your name with an initial investment of $5,900. You are turning 21 in a few days and will have access to all your funds. The account was earning 7.3 percent for the first seven years, but then the rates went down to 5.5 percent for six years. Your account then earned 8.2 percent three years in a row. Unfortunately, the next two years you earned only 4.6 percent. Finally, as the economy recovered, the return jumped to 7.6 percent for the last three years.

How much money was in your account before the rates went down drastically at the end of year 16? (If you solve this problem with algebra round intermediate calculations to 6 decimal places, in all cases round your input answers to the nearest penny.)

Investment value at age 16 years $_______________

How much money is in your account now, at the end of Year 21? (If you solve this problem with algebra round intermediate calculations to 6 decimal places, in all cases round your input answers to the nearest penny.)

Investment value at age 21 years

$______________

What would be the balance now if your parents made another deposit of $1,400 at the end of year 7? (If you solve this problem with algebra round intermediate calculations to 6 decimal places, in all cases round your input answers to the nearest penny.)

Balance at the end of year 7 $____________________

Answer 1

1.

Amount invested = $5,900

Interest rate for first 7 years = 7.3% = 0.073

Interest rate for next 6 years = 5.5% = 0.055

Interest rate for next 3 years = 8.2% = 0.082

Investment value at age of 16 years = $5,900 * 1.073⁷ * 1.055⁶ * 1.082³ = $16,875.11

2.

Interest rate for next 2 years = 4.6% = 0.046

Interest rate for last 3 years = 7.6% = 0.076

Investment value at age of 21 years = $16,875.11 * 1.046² * 1.076³ = $23,001

3.

Current value of amount invested at the end of year 7 = $1,400 * 1.055⁶ * 1.082³ * 1.046² * 1.076³ =$3,332.92

Total balance now = $23,001 + $3,332.92 = $26,333.92