Answer to Question #192486 in Financial Math for Glen Bezuidenhout

Question

Siphesihle borrows money from the bank at a discount rate of 16,5% per year. He must pay the bank R30 000 in eight months from now. The amount of money he receives from the bank now is

1.     R33 707,87.

2.     R26 700,00.

3.     R27 027,03.

4.     R33 463,26.

5.     R33 300,00

Answer 1

Solution:

Time, t = 8 months = 8/12 year = 2/3 year

Discount rate, r = 16.5% per year = 0.165

Let M be the borrowed money from the bank.

And D be the discounted amount.

Then, $D=M.r.t$

$\Rightarrow D=M(0.165)(2/3) \\\Rightarrow D=0.11M ...(i)$

Now, $P=30000$

$P=M-D \\ \Rightarrow 30000=M-0.11M$ [Using (i)]

$\Rightarrow 0.89M=30000 \\\Rightarrow M=33,707.87$

Hence, option 1, i.e., R 33707.87 is correct.