Question

If $7,500 is deposited at the end of every six months, with a compounding rate of 5.96% compounded semiannually, for a period of 7 years, what will be the future value of this investment?

A) $201,014.35
B) $113,553.31
C) $123,892.15
D) $423,892.15

Answer 1

The future value of a $7,500 biannual investment over 7 years at a 5.96% semiannual interest rate can be calculated using the future value of an annuity formula, resulting in approximately $376,502.48, where Option A is the closest to this value.

Step-by-step explanation:

To calculate the future value of an investment with a series of equal payments (annuities) and compound interest, we can use the future value of an annuity formula:

FV = P × rac{((1 + r)^n - 1)}{r}

Where:

• FV is the future value of the annuity.
• P is the payment amount per period.
• r is the interest rate per period.
• n is the total number of periods.

In this case:

• P = $7,500 (deposited every six months)
• r = 5.96% / 2 = 2.98% (since interest is compounded semiannually)
• n = 7 years × 2 = 14 periods (since there are two periods in a year)

Let's plug the values into the formula:

FV = $7,500 × rac{((1 + 0.0298)^14 - 1)}{0.0298}

Carrying out the calculations:

FV = $7,500 × rac{((1.0298)¹⁴ - 1)}{0.0298}

FV = $7,500 × 50.20033128 = $376,502.48

Option A is closest to this result. This example illustrates how compound interest can significantly increase the value of repeated investments over time as opposed to simple interest.