What is the annuity payable semi annually required to accumulate $5000 in 5years at the rate of 6% p.a
To find the annuity payment that needs to be made semi-annually to accumulate $5,000 in 5 years at an interest rate of 6% per annum, you first need to note that since payments are made semi-annually, the interest rate must be adjusted accordingly, as well as the number of periods.
The annual interest rate is 6%, so the semi-annual rate is 6% / 2 = 3% per period. There are 5 years x 2 periods per year = 10 semi-annual periods.
We can use the future value of an ordinary annuity formula to calculate the semi-annual payment (PMT):
FV = PMT × [(1 + r)^n - 1] / r
Where:
FV = Future Value of the annuity ($5,000)
PMT = The semi-annual payment we want to find
r = The interest rate per period (3% or 0.03)
n = The total number of payments (10)
Let's plug in the known values:
$5,000 = PMT × [(1 + 0.03)^10 - 1] / 0.03
First, calculate the part within the brackets:
(1 + 0.03)^10 - 1 = (1.03)^10 - 1 ≈ 1.343916379 - 1 ≈ 0.343916379
Now our equation becomes:
$5,000 = PMT × 0.343916379 / 0.03
Next, divide both sides of the equation by the result in the brackets:
PMT = $5,000 / (0.343916379 / 0.03)
PMT ≈ $5,000 / 11.4638793
PMT ≈ $436.19
Therefore, the semi-annual payment that needs to be made to accumulate $5,000 in 5 years at a 6% annual interest rate, with compounding semi-annually, is approximately $436.19.