Question

At age 24 , someone sets up an IRA (individual retirement account) with an APR of 5%. At the end of each month he deposits 100$ in the account. How much will the IRA contain when he retires at age 65? Compare that amount to the total deposits made over the time period. After retirement the IRA will contain $  (Do not round until the final answer. Then round to the nearest cent as needed.)

Answer 1

We would apply the formula for calculating the future value of an ordinary annuity. It is expressed as

S = R[((1 + i)^n - 1)/i

where

R is the payment at the end of each period

i is the interest rate per period

n is the number of periods

S is the future value

Since the deposit is monthly, i = r/12

where r is the interest rate

From the information given,

r = 5% = 5/100 = 0.05

i = 0.05/12 = 0.00417

R = 100

number of years = 65 - 24 =41

number of periods, n = 41 x 12 =492

By substituting these values into the formula, we have

S = 100[((1 + 0.00417)^492 - 1)/0.00417

S = 100[((1.00417)^492 - 1)/0.00417

S = 161637.31

The IRA will contain $161637.31 when he retires at 65

Total deposit made over the time period = 100 * 492 = $49200