Question

Explain without excel

(3) An amortized loan is repaid with annual payments which start at $400 at the end of the first year and increase by $45 each year until a payment of $1,480 is made, after which they cease. If interest is 4% effective, find the amount of principal in the fourteenth payment.

Answer 1

Annual payment at the end of first year = $ 400

each year increase = $45

Annual payment at the end of 14th year would be = $ 400 + ($45*13) i.e $400 + $585 i.e $985

( because each year $45 increases. so in the fourteenth payment, $45*13 should be added)

Now, this $985 amount includes interest @ 4%

so the principal amount would be $985/104* 100 i.e 947.11

(checking of answer: principal- 947.11, interest -4% therefore repayment = 947.11*4%= $ 985 which is the total repayment amount)