Answer to Question #196942 in Financial Math for Beauty Magadlela

Question

Tshepiso owes Thapelo R3 000, which is due ten months from now, and R25 000, which is due 32 months from now. Tshepiso asks Thapelo if she can discharge her obligations by two equal payments: one now and the other one 28 months from now. Thapelo agrees on condition that a 14,75% interest rate, compounded every two months, is applicable. The amount that Tshepiso will pay Thapelo 28 months from now is approximately

[1] R20 000.

[2] R14 000.

[3] R11 511.

[4] R11 907.

[5] R11 455.

Answer 1

Effective interest rate $=[1+\frac{rate}{n}]^{n}-1$

n denotes the compounding period

$=[1+\frac{0.1475}{6}]^{6}-1$

$=(1+0.02458)^{6}-1$

$=0.15685$

$=15.685\%$

Let two equal payments be X

Computation of X

PV of option 1 = PV of option 2

$\frac{R 3,000}{(1+\frac{15.685\%}{12})^{10}}+\frac{R 25,000}{(1+\frac{15.685\%}{12})^{32}}=X+\frac{X}{(1+\frac{15.685\%}{12})^{28}}$

$\frac{R 3,000}{(1+0.013071)^{10}} + \frac{R 25,000}{(1+0.013071)^{32}}=X+\frac{X}{(1+0.013071)^{28}}$

$\frac{R 3,,000}{(1+0.013071)^{10}}+\frac{R25,000}{(1+1.013071)^{32}}=X+\frac{X}{(1.013071)^{28}}$

$\frac{R3,000}{1.13867}+\frac{R25,000}{1.51522}=X+X(\frac{1}{1.43852})$

$R2,634.65+R16,499.25=X+X(0.69516)\\R19,133.90=X(1.69516)$

$X=\frac{R19,133.90}{1.69516}$

$=R11,287$

Hence, payment after will be R 11,287 which is approximately equals to R 11,455.

 

Hence, 5^th option is correct.

 

Note: -Answer may be vary due to intermediate round off.