Question

You 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 10.5% compounded quarterly.

What will strategy 1 accumulate at retirement?

		375913
		505445
		871993
		619066
		794343

Answer 1

In strategy 1 there are two parts which are as follows:

1. Investing money quaterly for 8 years

2. Then earning interest for next 21 years

Future value at 8 years = payment * ((1 + r)^n - 1)/r

payment = 1750

r = 10.5/4 %

= 2.625%

n = 33

Future value = 1750 * ((1.02625)^33 - 1)/.02625

= 1750 * (2.351552 - 1)/.02625

= 1750 * 51.4877

= 90103.475

Above value will give the interest over the next 21 years.

Value after 29 years = 90103.475 * (1 + r)^n

where r = 2.625%

n = 21*4 = 84

Value after 29 years = 90103.475 * (1.02625)^84

= 794343

Tus the correct answer is last option.