Question

An investment of $4889.98 earns interest at 3% per annum compounded semi-annually for 3 years. At that time the interest rate is changed to 19.5% compounded monthly. How much will the accumulated value be 3.5 years after the change?

The accumulated value is $ ___.

Answer 1

To calculate the accumulated value, we first calculate the value after 3 years with an interest rate of 3% compounded semi-annually, and then calculate how much that amount will grow for an additional 0.5 years with an interest rate of 19.5% compounded monthly. The accumulated value 3.5 years after the change will be $5895.23.

Step-by-step explanation:

To calculate the accumulated value after 3.5 years, we need to calculate how much the initial investment will grow until 3 years with an interest rate of 3% compounded semi-annually, and then calculate how much that amount will further grow for an additional 0.5 years with an interest rate of 19.5% compounded monthly.

For the first 3 years, the accumulated value can be calculated using the formula:

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

Substituting the given values:
A = 4889.98(1+0.03/2)^(2*3)
A = 4889.98(1.015)^6
A = 4889.98 * 1.093742424
A = $5343.02

For the remaining 0.5 years, the accumulated value can be calculated using the formula:

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

Substituting the given values:
A = 5343.02(1+0.195/12)^(12*0.5)
A = 5343.02(1.015416667)^6
A = 5343.02 * 1.101581256
A = $5895.23

Therefore, the accumulated value 3.5 years after the change will be $5895.23.