Question

A 20 year loan of $120, 000 at i = 6% is paid off by paying 130% of each year’s interest at the end of each year for the first 12 years, and then for the next 8 years pay off the loan by paying off constant principle at the end of each year. Find the value of the last payment.

Answer 1

Value of last payment is 12786

i am attaching a excel table in which calculations are done. All the formulas used are shown separately in the respective colored columns

In the above sheet

In first year

Interest payable is 120000*6% =7200, As per question 130% of interest(Assumed to be including interest amount) is paid in the respective year

130% of 7200 =9360. This is the total payment at the end of first year.

So Principal payment will be

Total payment - Interest payment

=9360-7200

=2160

This is done similarly for 12 years.

After 12 years i.e., in 13th year Balance principal to be paid is 96498, as per question equal principals are to be paid for the remaining 8 years.

Hence equated principals will be = 96498/8=12062

So every year 12062 is paid towards the principal portion

Interest in 13th year = 96498*6%=5790

Principal payment in 13th year = 12062

Total payment in 13th year =12062+5790=17852

Similarly it is done for remaining 8 years till

In 20th year beginning , balance principal to be paid will be 12062, hence interest is calculated on12062 @6% for 1 year

=120628*6%=724

724 is interest paid in 20th year and 12062 is the principal payment in 20th year.

Therefore total payment in 20th year is =724+12062

=12786