Question

An initial investment is $8614. It grows at a rate of 6% a year. Interest is compounded quarterly. What is the value after 5 years? Round your answer to the nearest penny.

Answer 1

The value after 5 years is approximately $10693.36.

Step-by-step explanation:

To calculate the value after 5 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal investment, r is the annual interest rate, n is the number of compoundings per year, and t is the time in years. In this case, the principal investment is $8614, the annual interest rate is 6%, and interest is compounded quarterly (n = 4). Plugging in these values, we get:

A = 8614(1 + 0.06/4)^(4 * 5)

Simplifying this equation, we have:

A = 8614(1.015)^20

Calculating this, we find that the value after 5 years is approximately $10693.36.