Question

A loan is being repaid over 10 years in equal annual installments. If the amount of principal in the third payment is $350, find the principal portion of the eighth payment given j₁₂ = 8.5% Ans; 534.56

Answer 1

Given

Principle Payment in third payment P3=$350

r=8.5%

N=10 years

Let P8 is Principle Payment in eight payment.

Let X be the balance principle at beginning of third year and y is per year installments.

So X=y*(1-(1+r)^-8)/r

X= y*(1-(1+8.5%)^-8/8.5%

X=5.64y

and interest payment in third year = X*8.5%=5.64y*8.5%=0.48y

Since P3=y-0.48y=0.52y

0.52y=350

y=$673.07

X=5.64*673.07=$3795.60

Balance principle at the beginning of eight year A=y*(1-(1+r)^-3)/r

A=673.07*(1-(1+8.5%)^-3)/8.5%

A=$1719.05

So Interest payment during eight year I8= A*8.5%=1719.05*8.5%=$146.12

Principle Payment in eight payment. P8=y-I=673.07-146.12=$526.95