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At age 25​, someone sets up an IRA​ (individual retirement​ account) with an APR of ​5%. At the end of each month he deposits ​$45 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.

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Answer:

As this is a constant amount being deposited, it is an annuity therefore the answer is the future value of the annuity.

65 -25= 40 years

Period = 40 * 12 months = 480

Interest = 5%/12

Amount in IRA upon retirement;

Future Value of Annuity = 45 * ([1 + 5%/12]^480 - 1 )/5%/12

= 45 * 1,526.02

= $68,670.9‬0

Deposits made over the time period = 45 * 40 * 12 = $‭21,600‬

Difference = 68,670.90 - 21,600 = $47,070.9‬0

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