Question

At age 20, someone sets up an IRA (individual retirement account) with an APR of 6%. At the end of each month he deposits $50 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 S
(Do not round until the final answer. Then round to the nearest cent as needed.)
The total deposits made over the time period is $
(Type a whole number.)

Answer 1

To calculate the amount in the IRA at retirement, we can use the formula for the future value of an annuity:

S = PMT * (((1 + r)^n - 1) / r)

Where:

PMT = the monthly payment (in dollars)

r = the monthly interest rate (APR/12)

n = the number of months (45 years * 12 months/year)

Substituting the given values, we get:

PMT = $50

r = 0.06/12 = 0.005

n = 45 * 12 = 540

S = $50 * (((1 + 0.005)^540 - 1) / 0.005) = $204,055.57

So the IRA will contain $204,055.57 at retirement.

The total deposits made over the time period is:

Total deposits = 540 * $50 = $27,000

Therefore, the amount in the IRA at retirement ($204,055.57) is significantly higher than the total deposits made over the time period ($27,000). This demonstrates the power of compound interest over a long time horizon

Explanation:

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