Question

Suppose a recent college graduate's first job allows her to deposit $150 at the end of each month in a savings plan that earns 9%, compounded monthly. This savings plan continues for 8 years before new obligations make it impossible to continue.

How much money has accrued in the account at the end of the 8 years? (Round your answer to the nearest cent.)

$

If the accrued amount remains in the plan for the next 15 years without deposits or withdrawals, how much money will be in the account 23 years after the plan began? (Round your answer to the nearest cent.)

$

Answer 1

Given that,

$150 is deposited in an account at the end of each month for next 8 years

interest rate r = 9% compounded monthly

So, final value in account is calculated using FV formula of ordinary annuity

=> FV = PMT*((1+r/n)^(n*t) - 1)/(r/n) = 150*((1+0.09/12)^(12*8) - 1)/(0.09/12) = $20978.42

money has accrued in the account at the end of the 8 years = $20978.42

If the accrued amount remains in the plan for the next 15 years without deposits or withdrawals

Account value in next 15 years is

Value at year 23 = FV*(1 + r/n)^(n*t) = 20978.42*(1 + 0.09/12)^(12*15) = $80516.10