Question

$650 is invested in an account earning 8.6% interest (APR), compounded monthly. Write a function showing the value of the account after tt years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.

Answer 1

The function is A = 650(1 + 0.086/12)^(12t). The annual growth rate is found by subtracting 1 from the rate of interest and multiplying by 100.

Step-by-step explanation:

Compound interest is calculated using the formula:

A = P(1 + r/n)^(nt)

Where:

• A is the future value of the investment
• P is the initial principal balance ($650)
• r is the annual interest rate (8.6% or 0.086)
• n is the number of times the interest is compounded per year (12 for monthly compounding)
• t is the number of years the money is invested for

To find the value of the account after tt years, we substitute the given values into the formula:

A = 650(1 + 0.086/12)^(12t)

To determine the percentage of growth per year (APY), we subtract 1 from the rate of interest and multiply by 100:

APY = (1 + 0.086/12)^12 - 1 * 100