Question

Stan wants to start an IRA that will have $250,000 in it when he retires in 25 years. How much should he invest semiannually in his IRA to do this if the interest is 6% compounded semiannually? Assume an Annuity Due. Round to the nearest cent.

Answer 1

To find out the amount Stan should invest semiannually to have $250,000 in 25 years at 6% interest compounded semiannually, the annuity due present value formula must be applied, taking into account that payments are made at the beginning of each period.

Step-by-step explanation:

The student's question revolves around determining how much Stan should invest semiannually in his Individual Retirement Account (IRA) to reach a goal of $250,000 in 25 years, with an interest rate of 6% compounded semiannually and using the Annuity Due formula. To solve this problem, the annuity due present value formula should be used:

P = R \[\frac{1 - (1 + r)^{-n}}{r}\] \times (1 + r)

Where P is the present value of the annuity due, R is the semiannual payment, r is the semiannual interest rate, and n is the number of periods.

Given that P = $250,000, r = 0.06/2 = 0.03, and n = 25 \times 2 = 50, we can solve for R.

Using the formula:

$250,000 = R \[\frac{1 - (1 + 0.03)^{-50}}{0.03}\] \times (1 + 0.03)

Calculating the result, and then rounding to the nearest cent, we will get the amount Stan needs to contribute semiannually.

Answer 2

$1,041,666.70 I'm not sure but that what I think the answer is