Question

ou are considering two different strategies for a savings account that you intend to close when you retire exactly 29 years from today. For Strategy 1, deposit $1,750 per quarter for 8 years (first deposit today; last one exactly 8 years from today); no new deposits will be made after the end of the deposit period, but interest continues to accrue until the account is closed. For Strategy 2, you’ll make your first quarterly deposit exactly 8 years from today, each quarterly deposit also equals $1,750 , and you’ll continue making quarterly deposits for 21 years, so that you make the final deposit exactly 29 years from today when you close the account. The savings rate always is 7.5% compounded quarterly. What will strategy 1 accumulate at retirement?

Answer 1

Strategy 1

For the first 8 years, this is annuity due (each payment is made at beginning of quarter) with 33 quarterly deposits.

Future value of annuity due = (1 + r) * P * [(1 + r)ⁿ - 1] / r,

where P = periodic payment. This is $1,750

r = periodic rate of interest. This is (7.5%/4). We divide by 4 since we need to convert the annual rate into quarterly rate)

n = number of periods. This is 33 (there are 33 quarterly deposits in the investment period)

Future value of annuity (at the end of 33 quarters from today) = (1 + (7.5%/4)) * $1,750 * [(1 + (7.5%/4))³³ - 1] / (7.5%/4)

Future value of annuity (at the end of 33 quarters from today) = $80,440.43

This amount compounds at 7.5% compounded quarterly for 20 years and 3 quarters, which is 83 quarters

Future value of lumpsum = present value * (1 + r)ⁿ

where n = number of periods. This is 83.

r = periodic rate of interest. This is (7.5%/4)

Future value = $80,440.43 * (1 + (7.5%/4))⁸³

Future value = $375,912.68

Strategy 1 will accumulate $375,912.68 at retirement