Question

You need 100.000   € to buy a flat. So, you go to the bank and ask for that amount. The bank offers an annual interest rate of 8%, and the loan has to be paid back in 5 years, in quarterly payments, so 1 payment every 3 months, frequency times per year, and by using the American system. Calculate how much you should pay to the bank every quarter.

Answer 1

	Quarterly rate(M)=	yearly rate/12=	2.00%	Quarterly payment=	6115.67
Quarter	Beginning balance (A)	Quarterly payment	Interest = M*A	Principal paid	Ending balance
1	100000.00	6115.67	2000.00	4115.67	95884.33
2	95884.33	6115.67	1917.69	4197.99	91686.34
3	91686.34	6115.67	1833.73	4281.94	87404.40
4	87404.40	6115.67	1748.09	4367.58	83036.81
5	83036.81	6115.67	1660.74	4454.94	78581.88
6	78581.88	6115.67	1571.64	4544.03	74037.84
7	74037.84	6115.67	1480.76	4634.91	69402.93
8	69402.93	6115.67	1388.06	4727.61	64675.32
9	64675.32	6115.67	1293.51	4822.17	59853.15
10	59853.15	6115.67	1197.06	4918.61	54934.54
11	54934.54	6115.67	1098.69	5016.98	49917.56
12	49917.56	6115.67	998.35	5117.32	44800.24
13	44800.24	6115.67	896.00	5219.67	39580.57
14	39580.57	6115.67	791.61	5324.06	34256.51
15	34256.51	6115.67	685.13	5430.54	28825.97
16	28825.97	6115.67	576.52	5539.15	23286.82
17	23286.82	6115.67	465.74	5649.94	17636.88
18	17636.88	6115.67	352.74	5762.93	11873.95
19	11873.95	6115.67	237.48	5878.19	5995.76
20	5995.76	6115.67	119.92	5995.76	0.00

Where

Interest paid = Beginning balance * Quarterly interest rate

Principal = Quarterly payment – interest paid

Ending balance = beginning balance – principal paid

Beginning balance = previous Quarter ending balance