Question

Fully amortized loan​ (annual payments for principal and interest with the same amount each​ year). Chuck Ponzi has talked an elderly woman into loaning him ​$35 comma 000 for a new business venture. She​ has, however, successfully passed a finance class and requires Chuck to sign a binding contract on repayment of the ​$35 comma 000 with an annual interest rate of 11​% over the next 5 years. Determine the cash flow to the woman under a fully amortized​ loan, in which Ponzi will make equal annual payments at the end of each year so that the final payment will completely retire the original ​$35 comma 000 loan.

Answer 1

Here loan amount = $35000

n = no of year = 5

Interest rate = r = 11%

Yearly installments = Loan/PVIFA(r%,n)

PVIFA(r%,n) = [1-(1/(1+r)^n / r ]
PVIFA(11%,5) = [1-(1/(1+11%)^5 / 11%]
=[1-(1/(1+0.11)^5 / 0.11]
=[1-(1/(1.11)^5 / 0.11]
=[1-0.59345 / 0.11]
=0.406549/0.11
=3.6959

Thus Yearly Installment = 35000/3.6959

= 9469.95 $

Amortization shcedule

Year	Opening balance	Installments	Interest @ 11%	Principal payments	Closing Blance
	A	B	C =A x 11%	D = B- C	E =A-D
1	35000.00	9469.95	3850.00	5619.95	29380.05
2	29380.05	9469.95	3231.81	6238.14	23141.91
3	23141.91	9469.95	2545.61	6924.34	16217.57
4	16217.57	9469.95	1783.93	7686.02	8531.55
5	8531.55	9469.95	938.47	8531.48	0

Thus yearly cash flows to elderly woman will be $ 9469.95

i.e $9470