Your company plans to borrow R 10 150 from today. Your company would like to repay the loan by making six semi-annual payments at the end of each payment period. What will the amount of each payment be if interest is compounded semi-annually at 8% p.a.?
To calculate the amount of each semi-annual payment, we can use the formula for calculating the payment amount for an amortizing loan:
PMT = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
PMT = payment amount
P = principal amount borrowed (R 10 150)
r = interest rate per period (8% per year compounded semi-annually = 4% per period)
n = total number of periods (6 semi-annual payments)
First, we find the interest rate per period:
r = 8% / 2 = 4% or 0.04
Next, we calculate the payment amount:
PMT = 10150 * 0.04 * (1 + 0.04)^6 / ((1 + 0.04)^6 - 1)
PMT = 10150 * 0.04 * (1.04)^6 / ((1.04)^6 - 1)
PMT = 10150 * 0.04 * 1.265319 / 1.265319 - 1
PMT = 10150 * 0.050613 / 0.265319
PMT = 513.171175 / 0.265319
PMT = R 1934.87
Therefore, the amount of each semi-annual payment will be R 1934.87.