A principal of $200 is invested at 5% interest rate annually. Determine the future value in 3 months' time if compounded:
(a) Semi-annually
(b) Quarterly
semi annually future value is $201.20
just use your formula. For quarterly, that is
200(1+.05/4)^(4*1/4) = 202.5
for semi-annually ....
amount = 200( 1.025)^(1/2) = 202.48 , not 201.20
5% compounded annually
To calculate the future value in 3 months' time, we need to determine the compounding frequency and use the appropriate formula.
(a) Semi-annually:
If the interest is compounded semi-annually, it means it is calculated and added twice a year. To calculate the future value, we can use the formula:
Future Value = Principal * (1 + (interest rate/compounding frequency)) ^ (compounding frequency * time)
In this case, the interest rate is 5%, which is 0.05 in decimal form. The compounding frequency is semi-annually, so it is 2. The time is 3 months, which is 1/4 of a year.
Future Value = $200 * (1 + (0.05/2))^ (2 * 1/4)
Future Value = $200 * (1 + 0.025)^0.5
Future Value = $200 * (1.025)^0.5
Future Value ≈ $203.14
Therefore, the future value in 3 months' time, compounded semi-annually, is approximately $203.14.
(b) Quarterly:
If the interest is compounded quarterly, it means it is calculated and added four times a year. Similarly, we can use the formula:
Future Value = Principal * (1 + (interest rate/compounding frequency)) ^ (compounding frequency * time)
Using the same interest rate of 5% (0.05 in decimal form) and the compounding frequency of 4, we can calculate the future value over 3 months:
Future Value = $200 * (1 + (0.05/4))^ (4 * 1/4)
Future Value = $200 * (1 + 0.0125)^1
Future Value ≈ $203.75
Therefore, the future value in 3 months' time, compounded quarterly, is approximately $203.75.