Answer to Question #316240 in Financial Math for Cherry

Question

Prince wants to open a Hair Salon and asks his uncle Lerumo if he wil l lend him the money. He also indicates that he wil l only be able to start paying him back after five years, at which time he wil l then pay R35 000 at the end of every four months, for four years. Uncle Lerumo agrees, on condition that his money must earn 12,2% interest per year,compounded every four months

1.The present value of Prin e's debt when he starts paying ba k un le Lerumo after 5 years will be?

2.The amount that Unc le Lerumo lends Prince is?

Answer 1

1) The present value, PV, is given as:

$PV=Pmt[\frac{1-(1+\frac{r}{m})^{-(mn)}}{\frac{r}{m}}]$

Where Pmt=R35000

N=5

M=3

R=0.122

$PV=R35000[\frac{1-(1+\frac{0.122}{3})^{-(5×3)}}{\frac{0.122}{3}}]$

$PV=R387335.79$

2) R35000×12

=R420000