Question

You invested $12,600 with an annual interest rate of 2.4% for the first 6 years. After that, you invested all the money and proceeds at 4.5% for the next 4 years. So, what was your annual rate of return over those 10 years?

Answer 1

To calculate the annual rate of return, compound interest for each period is computed separately and then combined to find the total growth, leading to the average annual rate over the 10 years.

Step-by-step explanation:

To determine the annual rate of return over the 10-year period where you invested $12,600 at an annual interest rate of 2.4% for the first 6 years and then reinvested at 4.5% for the next 4 years, you need to calculate the compound interest for each period and then find the overall growth factor to derive the average annual rate.

Firstly, you calculate the amount after 6 years using the formula for compound interest:

A1 = P(1 + r/n)^(nt)

Where:

• P = Principal amount ($12,600)
• r = Annual interest rate (2.4% or 0.024)
• n = Number of times interest is compounded per year (assumed to be 1 if not stated)
• t = Number of years (6)

After calculating A1, you will reinvest this amount at 4.5%:

• r = 4.5% or 0.045
• t = 4 years

Let's call the final amount A2. To find the overall rate, you use the formula:

(A2 / P) = (1 + overall rate)^10

Then solve for the 'overall rate' to find the average annual rate of return over the 10 years.