Question

Course- Theory of Interest (Chapter: Amortization and Sinking Funds)

A $75,000 loan to be repaid over a 5-year period, my be repaid by one of two methods

1) Level annual payments made at the beginning of each year

2) Level semi-annual payments made at the end of each 6-month period

If d^(4) = 0.076225, Find the absolute difference in the payments made each year under the two methods.

Answer: $1,030.22

Answer 1

Given

Loan Amount P=$75000

Years =5

Interest rate =0.076225

A)

Let A be Payment made at beginning of the year

So r=0.07225

N=5

So A=P*r/{(1-(1+r)^-N)*(1+r)}

A=75000*0.07225/{(1-(1+0.07225)^-5)*(1+0.07225)}

A=$17280.51 Eq 1

B)

Let S be Payment made at end of each 5 month

So r=0.07225/2=0.0381125

N=5*2=10

So S=P*r/{(1-(1+r)^-N)*(1+r)}

S=75000*0.0381125/{(1-(1+0.0381125)^-10)*(1+0.0381125)}

S=$9160.14

Payment made in a year =2*9160.14 =$18320.28 Eq 2

So from Equation 2 and 3 we find that difference between two methods is

18320.28-17280.51=$1039.77