1. To calculate Thabo's half yearly payments, we can use the formula for calculating the regular payment on a loan:
Payment = Principal * (r(1 + r)^n) / ((1 + r)^n - 1)
Where:
Principal = R80000
r = (0.18/2) = 0.09 (interest rate divided by 2 for semi-annual compounding)
n = 5 years * 2 semi-annual payments per year = 10 payments
Plugging in the values:
Payment = R80000 * (0.09(1 + 0.09)^10) / ((1 + 0.09)^10 - 1)
Payment = R80000 * (0.09(2.17200491)) / (2.17200491 - 1)
Payment = R80000 * (0.19548044) / 1.17200491
Payment = R80000 * 0.16691408
Payment = R13353.13
Therefore, Thabo's half yearly payments are R13353.13.
2. After the 10th payment, Thabo would owe an amount equal to the present value of the remaining payments. To calculate that, we can use the formula for the present value of an annuity:
PV = Payment * ((1 - (1 + r)^-n) / r)
Where:
Payment = R13353.13
r = 0.09
n = 5 years * 2 payments per year - 10 payments made = 10 remaining payments
Plugging in the values:
PV = R13353.13 * ((1 - (1 + 0.09)^-10) / 0.09)
PV = R13353.13 * ((1 - (1.09)^-10) / 0.09)
PV = R13353.13 * ((1 - 0.422274) / 0.09)
PV = R13353.13 * (0.577726 / 0.09)
PV = R13353.13 * 6.41917778
PV = R85786.39
Therefore, Thabo would owe R85786.39 immediately after the 10th payment.
Thabo pays off loan of R80000over a period of 5 years.he makes half yearly payments starting after six months after the loan was granted and ending at the end of 5 year period .the interest rate is 18% p.a compounded semi annually
1 .what is his half yearly payments?
2 .how much does he owe immideately after 10th payments?
1 answer
1 answer