Question

A person borrows $40000 at an interest rate of 9% per year. It is desired to repay the loan in 10 payments, with the first payment 3 years from now. If the payments are to increase by $200 each time, determine the size of the first payment.

Answer 1

Total loan amount           =             $40,000.00

First installment made in 3 years from now.

Let X be the first installment amount.

The formula to compute First installment:

$40,000 = X*[(A/P, 9%,13years) – (A/P,9%,2years)] + Present value of incremental cash flows

$40,000 = X*(7.4868 – 1.7591) + $4,755.06

$40,000 = X*(5.7277) + $4,755.06

X*(5.7277)          = $40,000 - $4,755.06

X*(5.7277)          = $35,244.94

X             = $35,244.94 / 5.7277

X             = $6,153.419

Therefore, First installment in the year 3 is $6,153.419

Working Notes: Present value of Incremental cash flows:

Incremental cash flows will from year 4. Loan payment will increase by $200.00 per year.

Year	Cash Flows ($)	PVF @9%	Discounted Cash Flows($)
4	200.00	0.7084	141.68
5	400.00	0.6499	259.96
6	600.00	0.5963	357.78
7	800.00	0.5470	437.60
8	1000.00	0.5019	501.90
9	1200.00	0.4604	552.48
10	1400.00	0.4224	591.36
11	1600.00	0.3875	620.00
12	1800.00	0.3555	639.90
13	2000.00	0.3262	652.40
TOTAL			4,755.06