What quarterly compounded rate of return will allow investments of $800 at the end of every six months to accumulate to $24,000 after 10 years?

Question

Quizplus · Accepted Answer

The correct approach to solve this problem involves using the formula for the future value of a series of annuity payments compounded quarterly. However, since the payments are made semi-annually, and the compounding is quarterly, we need to adjust our calculations accordingly. The formula for the future value of an annuity compounded differently from payment frequency is not straightforward and typically requires numerical methods or financial calculators for precise solutions. Given the options, we can infer or use a financial calculator to find the closest matching rate. The correct answer, after performing the calculations or using a financial calculator with the given parameters (future value = $24,000, payment = $800, periods = 20 since payments are semi-annual over 10 years, and compounding quarterly), is approximately 8.062%, which corresponds to choice B. This rate of return, when applied correctly, will allow the investments to accumulate to the desired amount under the given conditions.

What Quarterly Compounded Rate of Return Will Allow Investments of $800