Question

A couple who borrow $50,000 for 15 years at 8.4%, compounded monthly, must make monthly payments of $489.44. (Round your answers to the nearest cent.) (a) Find their unpaid balance after 1 year. $ (b) During that first year, how much interest do they pay? $

Answer 1

a.

There are 12 months in a year. Since the rate is yearly, it is divided by 12 in order to get it monthly. Ending balance of a month would be the beginning balance of the coming month.

Therefore, calculations in each month are calculated below:

Month	Beginning balance	Interest paid	Principal paid	Ending unpaid balance
1	50,000	50,000 × 8.4% × (1/12) = 350	489.44 – 350 = 139.44	50,000 – 139.44 = 49,860.56
2	49,860.56	49860.56 × 8.4% × (1/12) = 349.02	489.44 – 349.02 = 140.42	49,860.56 – 140.42 = 49,720.14
3	49,720.14	49720.14 × 8.4% × (1/12) = 348.04	489.44 – 348.04 = 141.40	49,720.14 – 141.40 = 49578.74
4	49,578.74	347.05	142.39	49,436.34
5	49,436.34	346.05	143.39	49,292.95
6	49,292.95	345.05	144.39	49,148.56
7	49,148.56	344.04	145.40	49,003.16
8	49,003.16	343.02	146.42	48,856.74
9	48,856.74	342.00	147.45	48,709.29
10	48,709.29	340.97	148.48	48,560.81
11	48,560.81	339.93	149.52	48,411.29
12	48,411.29	338.88	150.56	48,260.73
Total		$4,134.05

Answer: the ending unpaid balance after 1 year is $48,260.73.

b.

Answer: $4,134.05

The total column in the table above gives the amount of interest paid during the year.