Question

Find the monthly payment and estimate the remaining balance. Assume interest is on the unpaid balance. 4-year computer loan for $2270 at 7.4%; remaining balance after 2 years. The monthly payment is $ (Round to the nearest cent as needed.)

I need to know the monthly payment, and balance

Answer 1

Solution

To calculate the monthly payment amount, we will have to use the following equation,

P x {[ r x (1+r)ⁿ ] / [ (1+r)ⁿ -1 ]}

Where,

P = Amount of Loan = $ 2270

r = Annual Interest / 12 = 7.40% / 12 = 0.6167% (Approx.), or 0.006167

n = Number of Payments = 4 x 12 = 48

Therefore,

Monthly Payments = 2270 x { [ 0.006167 x (1.006167) ⁴⁸ ] / [ (1.006167) ⁴⁸ - 1]}

= 2270 x [ (0.006167 x 1.3433) / (1.3433 – 1) ] [Where (1.006167) ⁴⁸ = 1.3433 (Approx.)]

= 2270 x (0.008284 / 0.3433) [Where (0.006167 x 1.3433) = 0.008284 (Approx.)]

= 2270 x 0.02413 [Where (0.008284 / 0.3433) = 0.02413 (Approx.)]

= 54.78 (Approx.)

Therefore, Monthly Payments will be $54.78

Now as we have the monthly payments, we can draw a table as follows,

Terms	Opening Balance	Interest @ 0.6167%	Repayments	Closing Balance
	(1)	(2) = (1) x 0.6167%	(3)	(4) = (1) + (2) – (3)
1	$ 2,270.00	$       14.00	$     54.78	$ 2,229.22
2	$ 2,229.22	$       13.75	$     54.78	$ 2,188.19
3	$ 2,188.19	$       13.49	$     54.78	$ 2,146.90
4	$ 2,146.90	$       13.24	$     54.78	$ 2,105.36
5	$ 2,105.36	$       12.98	$     54.78	$ 2,063.56
6	$ 2,063.56	$       12.73	$     54.78	$ 2,021.51
7	$ 2,021.51	$       12.47	$     54.78	$ 1,979.20
8	$ 1,979.20	$       12.21	$     54.78	$ 1,936.62
9	$ 1,936.62	$       11.94	$     54.78	$ 1,893.79
10	$ 1,893.79	$       11.68	$     54.78	$ 1,850.69
11	$ 1,850.69	$       11.41	$     54.78	$ 1,807.32
12	$ 1,807.32	$       11.15	$     54.78	$ 1,763.68
13	$ 1,763.68	$       10.88	$     54.78	$ 1,719.78
14	$ 1,719.78	$       10.61	$     54.78	$ 1,675.61
15	$ 1,675.61	$       10.33	$     54.78	$ 1,631.16
16	$ 1,631.16	$       10.06	$     54.78	$ 1,586.44
17	$ 1,586.44	$         9.78	$     54.78	$ 1,541.44
18	$ 1,541.44	$         9.51	$     54.78	$ 1,496.17
19	$ 1,496.17	$         9.23	$     54.78	$ 1,450.62
20	$ 1,450.62	$         8.95	$     54.78	$ 1,404.78
21	$ 1,404.78	$         8.66	$     54.78	$ 1,358.67
22	$ 1,358.67	$         8.38	$     54.78	$ 1,312.26
23	$ 1,312.26	$         8.09	$     54.78	$ 1,265.58
24	$ 1,265.58	$         7.80	$     54.78	$ 1,218.60
25	$ 1,218.60	$         7.52	$     54.78	$ 1,171.34
26	$ 1,171.34	$         7.22	$     54.78	$ 1,123.78
27	$ 1,123.78	$         6.93	$     54.78	$ 1,075.93
28	$ 1,075.93	$         6.64	$     54.78	$ 1,027.79
29	$ 1,027.79	$         6.34	$     54.78	$     979.34
30	$     979.34	$         6.04	$     54.78	$     930.60
31	$     930.60	$         5.74	$     54.78	$     881.56
32	$     881.56	$         5.44	$     54.78	$     832.22
33	$     832.22	$         5.13	$     54.78	$     782.57
34	$     782.57	$         4.83	$     54.78	$     732.62
35	$     732.62	$         4.52	$     54.78	$     682.36
36	$     682.36	$        4.21	$     54.78	$     631.78
37	$     631.78	$         3.90	$     54.78	$     580.90
38	$     580.90	$         3.58	$     54.78	$     529.70
39	$     529.70	$         3.27	$     54.78	$     478.19
40	$     478.19	$         2.95	$     54.78	$     426.36
41	$     426.36	$         2.63	$     54.78	$     374.21
42	$     374.21	$         2.31	$     54.78	$     321.74
43	$     321.74	$         1.98	$     54.78	$     268.94
44	$     268.94	$         1.66	$     54.78	$     215.82
45	$     215.82	$         1.33	$     54.78	$     162.37
46	$     162.37	$         1.00	$    54.78	$     108.59
47	$     108.59	$         0.67	$     54.78	$       54.48
48	$       54.48	$         0.30	$     54.78	$              -

Here we need to check the balance at the end of 2^nd year, i.e. after the 24^th payment, which is $1218.60

Therefore, balance at the end of 2^nd year will be $1218.60