Question

Suppose that you are interested in borrowing $5300 for the purchase of a second hand car. Suppose that you would like to make fix amount quarterly payments (making the first payment by the end of the first quarter), and that you want to be debt free by the end of 7 and a half (7.5) years.

If the interest rate charged by the bank is 4.6%, then:

The quarterly amount that you would have to pay for this loan is: $Answer

Answer 1

Loan amount		$5,300
Frequency of payment	Quarterly
Tenor		7.5 years
No. of quarters	30	(7.5 x 4)
Interest rate		4.60%
Interest per quarter	1.15%	(4.6%/4)
In excel, fixed instalment can be calculated using the formula - PMT
=pmt (rate per period, number of periods, -loan amount)
=pmt(1.15%, 30, -5,300)
$209.89
Hence, quarterly instalment is $209.89
Let's verify this in the below table
A	B	C (Closing Principal * 1.15%)	D	E
Quarter	Instalment	Interest on Principal	Principal = B - C	Closing Principal
1	$209.89	$60.95	$148.94	$5,151.06	(60.95 = 5,300 * 1.15%)
2	$209.89	$59.24	$150.66	$5,000.40
3	$209.89	$57.50	$152.39	$4,848.01
4	$209.89	$55.75	$154.14	$4,693.87
5	$209.89	$53.98	$155.92	$4,537.95
6	$209.89	$52.19	$157.71	$4,380.24
7	$209.89	$50.37	$159.52	$4,220.72
8	$209.89	$48.54	$161.36	$4,059.37
9	$209.89	$46.68	$163.21	$3,896.15
10	$209.89	$44.81	$165.09	$3,731.06
11	$209.89	$42.91	$166.99	$3,564.08
12	$209.89	$40.99	$168.91	$3,395.17
13	$209.89	$39.04	$170.85	$3,224.32
14	$209.89	$37.08	$172.81	$3,051.50
15	$209.89	$35.09	$174.80	$2,876.70
16	$209.89	$33.08	$176.81	$2,699.89
17	$209.89	$31.05	$178.85	$2,521.04
18	$209.89	$28.99	$180.90	$2,340.14
19	$209.89	$26.91	$182.98	$2,157.16
20	$209.89	$24.81	$185.09	$1,972.07
21	$209.89	$22.68	$187.22	$1,784.86
22	$209.89	$20.53	$189.37	$1,595.49
23	$209.89	$18.35	$191.55	$1,403.94
24	$209.89	$16.15	$193.75	$1,210.19
25	$209.89	$13.92	$195.98	$1,014.22
26	$209.89	$11.66	$198.23	$815.98
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