Question

An investment of $2329.58 earns interest at 3.9% per annum compounded quarterly for 4 years. At that time the interest rate is changed to 15% compounded monthly. How much will the accumulated value be 3 years after the change?

Answer 1

To calculate the accumulated value 3 years after the interest rate change, first calculate the value after the first 4 years with the initial interest rate of 3.9% compounded quarterly. Then calculate the value for the remaining 3 years with the new interest rate of 15% compounded monthly. The accumulated value will be $3391.02.

Step-by-step explanation:

To calculate the accumulated value 3 years after the interest rate change, we need to calculate the value after the first 4 years with the initial interest rate of 3.9% compounded quarterly, and then calculate the value for the remaining 3 years with the new interest rate of 15% compounded monthly.

First, let's calculate the value after the first 4 years with the initial interest rate:

1. Convert the interest rate of 3.9% per annum to a quarterly rate: 3.9% / 4 = 0.975%.
2. Convert the time period of 4 years to the number of quarters: 4 * 4 = 16 quarters.
3. Use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the accumulated value, P is the principal amount, r is the interest rate, n is the number of compounding periods per year, and t is the number of years. Plug in the values and calculate: A = $2329.58(1 + 0.00975/4)^(4*16) = $2634.41.

Next, let's calculate the value for the remaining 3 years with the new interest rate:

1. Convert the interest rate of 15% per annum to a monthly rate: 15% / 12 = 1.25%.
2. Convert the time period of 3 years to the number of months: 3 * 12 = 36 months.
3. Use the same formula for compound interest: A = P(1 + r/n)^(nt), where A is the accumulated value, P is the principal amount, r is the interest rate, n is the number of compounding periods per year, and t is the number of years. Plug in the values and calculate: A = $2634.41(1 + 0.0125/12)^(12*3) = $3391.02.

Therefore, the accumulated value 3 years after the change in interest rate will be $3391.02.