Question

Laura wants to start an IRA that will have $310,000 in it when she retires in 15 years. How much should she invest monthly in her IRA to do this if the interest is 5% compounded monthly?

A $1,146. 79

B. $1,159. 79

C. $24,787. 10

D. $2,007. 6

Answer 1

A.

Explanation:

To find out how much Laura should invest monthly in her IRA to reach a balance of $310,000 in 15 years with a 5% interest compounded monthly, we can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

Where:

FV = Future Value (desired balance) = $310,000

P = Monthly investment

r = Monthly interest rate = 5% / 100% = 0.05 / 12 = 0.0041667

n = Number of periods = 15 * 12 = 180

Plugging these values into the formula, we have:

$310,000 = P * ((1 + 0.0041667)^180 - 1) / 0.0041667

Now, we can solve for P:

P = $310,000 * 0.0041667 / ((1 + 0.0041667)^180 - 1)

Calculating this expression, we find:

P ≈ $1,146.79