Compound Interest Calculation Example with Changing Interest Rates

a. What is the accumulated value of the investment at the end of year 1?

b. What is the accumulated value of the investment at the end of year 3 if the interest rate changes to 3.75% compounded monthly at the end of year 1?

c. How much interest was earned from this investment during the 3-year period?

a. Answer:

b. Answer:

c. Answer:

Compound interest is a powerful tool that helps in calculating the growth of an investment over time. In this example, we start with an initial investment of $15,000 growing at 3.25% compounded quarterly.

a. Accumulated Value at the end of Year 1:

The accumulated value of the investment at the end of year 1 can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt). Given the initial principal of $15,000, an annual interest rate of 3.25% (0.0325 as a decimal), and quarterly compounding (n = 4), the calculation becomes:

A = $15,000(1 + 0.0325/4)^(4*1)

A ≈ $15,000(1.008125)^4

A ≈ $15,000(1.033074)

A ≈ $15,496.11

Therefore, the accumulated value of the investment at the end of year 1 is approximately $15,496.11.

b. Accumulated Value at the end of Year 3:

If the interest rate changes to 3.75% compounded monthly at the end of year 1, the accumulated value at the end of year 3 can be calculated using the new interest rate and compounding frequency. Using the previous accumulated value ($15,496.11) as the new principal, an annual interest rate of 3.75% (0.0375 as a decimal), and monthly compounding (n = 12), the calculation is:

A = $15,496.11(1 + 0.0375/12)^(12*2)

A ≈ $15,496.11(1.003125)^24

A ≈ $15,496.11(1.082764)

A ≈ $16,762.10

Therefore, the accumulated value of the investment at the end of year 3 is approximately $16,762.10.

c. Amount of Interest Earned:

To find the amount of interest earned during the 3-year period, we can subtract the initial principal from the accumulated value at the end of year 3:

Interest = Accumulated Value - Principal

Interest = $16,762.10 - $15,000

Interest ≈ $1,762.10

Thus, the amount of interest earned from this investment during the 3-year period is approximately $1,762.10.