Question

A bank markets the following product. You take out a loan today and then repay 2,000 for eight years and 3,000 for another eight years (so that there are 16 payments total). If the interest rate is 4%, what is the size of the loan?

Answer 1

Calculation of size of the loan
We need to find out the present value of all future loan payments using discount rate of 4%
Year	Loan payments	Discount factor @ 4%	Present Values
1	$2,000.00	0.961538	$1,923.08
2	$2,000.00	0.924556	$1,849.11
3	$2,000.00	0.888996	$1,777.99
4	$2,000.00	0.854804	$1,709.61
5	$2,000.00	0.821927	$1,643.85
6	$2,000.00	0.790315	$1,580.63
7	$2,000.00	0.759918	$1,519.84
8	$2,000.00	0.73069	$1,461.38
9	$3,000.00	0.702587	$2,107.76
10	$3,000.00	0.675564	$2,026.69
11	$3,000.00	0.649581	$1,948.74
12	$3,000.00	0.624597	$1,873.79
13	$3,000.00	0.600574	$1,801.72
14	$3,000.00	0.577475	$1,732.43
15	$3,000.00	0.555265	$1,665.79
16	$3,000.00	0.533908	$1,601.72
Size of the loan			$28,224.14