Answer to Question #197949 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 amount of money that aunt Magda originally lent Bonita is

[1] R130 288,26.

[2] R186 054,89.

[3] R184 589,43.

[4] R98 346,23.

[5] R130 633,09

Answer 1

Solution:

Given, $P=R\ 105,000,\ r=19.5\%=0.195, n=5, t=3$

It is a deferred annuity.

$A=P\times[\dfrac{1-(1+r)^{-n}}{(1+r)^t\times r}] \\=105000\times [\dfrac{1-(1+0.195)^{-5}}{(1+0.195)^3\times 0.195}] \\=186054.883 \\\approx R\ 186054.89$

Hence, option 2 is correct.