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 6.5% compounded quarterly. What will strategy 1 accumulate at retirement?

Answer 1

Given retirement age in = 29 years

Quarterly Annuity (A) = 1750$

Number of years(m) = 8 years

Frequency(n) = 4 times in an year

savings rate (r) = 6.5%

This type of annuity is annuity due. Future Value Annuity due formula is as follows

Future Value Annuity at the end of year 8= (1+(r/m)*A*{(((1+(r/m))^(m*n) - 1) /(r/m)}

= (1+(0.065/4))*1750*{(((1+(0.065/4))^(8*4) - 1)/(0.065/4)}

=1778.4375 * (41.5392)

= 73,874.8510$

Still for his retirement he has 21 years that is 29-8 = 21 years on which he earns savings rate

there fore future value of his investment = present value at 8th year *(1+rate)^21

=73,874.8510*(1+0.065)^21

=271,813.3636$

Amount that he gets at the time of retirement = 271,813.3636$