To find the value of the semi-annual payments, we can use the formula for the present value of an annuity:
PV = PMT * (1 - (1 + r)^-n) / r
Where:
PV = Present value of the loan (R15,000)
PMT = Semi-annual payment
r = Interest rate per period (0.09, since it is compounded semi-annually)
n = Number of periods (4.5 years * 2 semi-annual payments per year = 9 periods)
Plugging in the values:
15,000 = PMT * (1 - (1 + 0.09)^-9) / 0.09
15,000 = PMT * (1 - (1.09)^-9) / 0.09
15,000 = PMT * (1 - 0.472) / 0.09
15,000 = PMT * (0.528) / 0.09
PMT = 15,000 / 0.0472
PMT ≈ R2 635.64
Therefore, the value of the semi-annual payments is R2 635.64.
An outstanding short-term loan of R15 000 is to be discharged by a series of equal semi-annually payments over 4 and a half years, the first being made immediately. If the interest rate is 18% p.a. compounded semi-annually, find the value of the semi-annual payments.
R 2 295.40
R 2 970.34
R 2 461.67
R 2 635.64
1 answer