Answer to Question #197948 in Financial Math for Beauty Magadlela

Question

Bonita intends to open a small fabric shop and borrows the money for it from her aunt Magda. Bonita feels that she will only be able to start repaying her debt after three years. Bonita will then pay aunt Magda R105 000 per year for five years. Money is worth 19,5% per year.

The present value of Bonita’s debt at the time she will start paying aunt Magda back is

[1] R408 978,93.

[2] R317 500,78.

[3] R222 924,04.

[4] R525 000,00.

[5] R436 649,07.

Answer 1

A loan is a financial term that indicates an amount borrowed by one person from another person at a predetermined financial charge. The borrower shall be required to repay the principal amount and interest accrued either on a periodic basis or in a lump-sum amount. 

When a loan is repaid on a periodic basis, then each periodic payment shows an equivalent uniform periodic cash flow which contains both principal part and accrued interest. The loan balance at any point in time shows the present value of all equivalent uniform periodic cash flows discounted at the effective interest rate. 

In this case, the present value of the loan can be determined as a sum of the present value of future cash flows discounted at 19.5%. It can be done by using the present value of an annuity formula. 

Calculating the present value of the annuity:

$Present \space value=P\times\frac{1-(1+r)^{-n}}{r}$

$=105, 000\times\frac{1-(1+0.195)^{-5}}{0.195}$

$=317,500.78$

Where:

The annual payment (P) is 105,000,

The annual discount rate (r) is 19.5%,

The total number of annual payments (n) is 5.

 

Thus, option (2) is correct, i.e., the present value of the loan is 317,500.78.