Question

Suppose a recent college graduate's first job allows her to deposit $250 at the end of each month in a savings plan that earns 9%, compounded monthly. This savings plan continues for 13 years before new obligations make it impossible to continue. 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 28 years after the plan began? (Round your answer to the nearest cent.)

Answer 1

We will use the following formulae.

1. The future value (F) of an annuity is given by F = (P/r)[(1+r)ⁿ-1], where P is the periodic payment , r is the rate per period and n is the number of periods.

2. The formula for maturity value (F) of an initial deposit (P), after n years, where interest rate is r % and interest is compounded t times per year is F = P(1+r/100t)^nt.

Since the college graduate deposits $250 at the end of each month in a savings plan that earns 9%, compounded monthly, for 13 years, hence P = 250, r = 9/1200 and n = 13*12 = 156. Therefore, F = (250*1200/9)[ 1+9/1200)¹⁵⁶ -1] = (100000/3)*0.519578253 = $ 51957.83 ( on rounding off to the nearest cent).

Thus, the balance in the student’s a/c at the end of 13 years is $ 51957.83.

The maturity value of $ 51957.83 , if kept in an account for the next 15 years on the terms mentioned earlier is 51957.83(1+ 9/1200)^15*12 = 51957.83*(1.0075)¹⁸⁰ = 51957.83*3.838043267 = $ 199416.40( on rounding off to the nearest cent).

Thus, the balance in the student’s a/c at the end of 28 years will be $ 199416.40.