John invests RM25000 in an account for 8 years. The investment account pays 8% compounded
semi-annually for the first three years and 10% compounded quarterly for the rest of the period.
i. Calculate the future value of the investment
ii. Compute the interest earned from John’s investment.
"The investment account pays 8% compounded semi-annually for the first three years"
---> 6 interest periods at a rate of .04
" 10% compounded quarterly for the rest of the period."
-----> 20 interest periods at .025 per period
amount = 25000(1.04)^6 (1.025)^20
= ....
To calculate the future value of the investment, we can use the formula for compound interest:
Future Value = Principal (1 + Interest Rate / n)^(n * Years)
Where:
- Principal = RM25000 (The initial amount invested)
- Interest Rate = 8% (compounded semi-annually for the first three years) and 10% (compounded quarterly for the remaining 5 years)
- n = Number of times interest is compounded per year
- Years = 8 (The total investment period)
Let's calculate the future value of the investment:
For the first three years where the interest rate is 8% compounded semi-annually:
n = 2 (since it's compounded semi-annually)
Future Value = 25000 (1 + 0.08/2)^(2 * 3) = 25000 (1 + 0.04)^6
For the remaining five years where the interest rate is 10% compounded quarterly:
n = 4 (since it's compounded quarterly)
Future Value = 25000 (1 + 0.1/4)^(4 * 5) = 25000 (1 + 0.025)^20
Now, we can calculate the future value of the investment by multiplying the two results:
Future Value = 25000 (1 + 0.04)^6 * 25000 (1 + 0.025)^20
To compute the interest earned from John's investment, we subtract the initial principal from the future value:
Interest Earned = Future Value - Principal
Now, inputting the values, you can calculate the future value and the interest earned from John's investment.