Answer to Question #310272 in Financial Math for LINDIE

Question

To pay off a loan of R7 000 due now and a loan of R2 000 due in 14 months' time, Olorato agrees to make three payments in two, five and ten months' time respectively. The second payment is to be double the first and the third payment is to be triple the first. What is the size of the payment at month five if interest is calculated at 16% per year, compounded monthly?

Answer 1

Assume first payment to be X. Hence, present value of X, 2X and 3X must be equal to present value of 7000 and 2000

$PVF(r,n)$ $(1/(1+r) )^n$

where PVF is present value factor, r is monthly rate and n is month

$X PVF(\frac{16\%}{12.2}) + 2X PVF(\frac{16\%}{12.5}) + 3X PVF(\frac{16\%}{12.10}) 7000 + 2000 PVF(\frac{16\%}{12.14})$

$X 0.97386 + X 1.87184 + X 2.62783 = 7000 + 2000 x 0.83074$

$X 5.47353 = 8661.48$

$X =\frac{8661.48 }{1582.43 5.47353}$

Payment month 5 = 2X = 2 x 1582.43 3164.86