Question

Lauren deposited $14,500 into a fund at the beginning of every quarter for 16 years. He then stopped making deposits into the fund and allowed the investment to grow for 4 more years. The fund was growing at 4.53% compounded monthly.

a. What was the accumulated value of the fund at the end of year 16?

b. What was the accumulated value of the fund at the end of year 20?

c. What is the total amount of interest earned over the 20-year period?

Answer 1

Periodic deposit = $14,500

Initial Investment period = 16 years = 16*4 quarters = 64 quarters

Annual Interest Rate = 4.53%

Monthly interest rate = 4.53%/12 = 0.3775%

Quarterly interest rate = (1+monthly interest rate)³ -1 = (1+0.3775%)³ -1 = 1.011368 -1

= 0.011368 = 1.1368%

a)

accumulated value of the fund at the end of year 16 can be calculated using FV function in spreadsheet

FV(rate, number of periods, payment amount, present value, when-due)

Where, rate = Quarterly interest rate = 1.1368%

number of periods = 64 quarters

payment amount = Periodic deposit = $14,500

present value = present value of investments = 0

when-due = when is the investment made each year = beginning = 1

accumulated value of the fund at the end of year 16 = FV(1.1368%, 64, -14500, 0, 1) = $1,369,382.52

b)

accumulated value of the fund at the end of year 20 = accumulated value of the fund at the end of year 16 *(1+annual interest rate)⁴ = $1,369,382.52 *(1+4.53%)⁴ = $1,634,890.17

c)

Total amount invested in 16 years = periodic deposit * number of deposits made = $14,500 * 64 = $928,000

Interest earned over 20 years = accumulated value of the fund at the end of year 20 - Total amount invested in 16 years = $1,634,890.17 - $928,000 = $706,890.17