Question

Jolene set up a retirement account. She arranged to have $350 taken out of each of her monthly checks; the account will earn 2.1% interest compounded monthly. She just turned 33, and her ordinary annuity comes to term when she turns 60. Find the value of her retirement account at that time.

Answer 1

A convenient formula to use is

S = ((1 + i)^n - 1) / i where S is the value of 1$ deposited for n periods at an interest rate of i

in this case n = 12 * 28 = 336 periods of deposit at an interest rate of

.0021 / 12 = .00175 = i

S = (1.00175^336 - 1) / .00175 = 456.8338 the value of 1$ after 336 periods

350 * 456.8338 = 159891.81 the value of 350 deposited monthly

Note that 350 * 336 would be 117,600

One must be careful to distinguish the above formula from

(1 - (1 + i)^-n) / i which gives the value of 1$ when the borrower is "paying" an interest rate of i - this would be the case for a mortgage - or what is the value of 1$ paid for n periods when paying an interest rate of i