Question

How much can you borrow if you are willing to make a single payment of 100,000 twelve years from now and the lender will charge 6% annual interest, compounded quarterly? what is the total amount of interest you will pay

Answer 1

Interest rate Annually = 6%

Therefore for Quarterly = 4 months / 12 months * 6% = 1.5%

Number of times Interest is to be charged = 12 years * 4 Quarters = 48 quarters

Amount Borrowed today = = 0.48936 *100000 = 48936

Excel Formula = (1/(1+(1*1.5/100))^48)*100000

Total Interest to be paid = 100000-48936 = 51064

Following is a table for reference

No of Quarters	Principle	Interest	Cumulative
1	48,936	734	49,670
2	49,670	745	50,415
3	50,415	756	51,171
4	51,171	768	51,939
5	51,939	779	52,718
6	52,718	791	53,509
7	53,509	803	54,311
8	54,311	815	55,126
9	55,126	827	55,953
10	55,953	839	56,792
11	56,792	852	57,644
12	57,644	865	58,509
13	58,509	878	59,386
14	59,386	891	60,277
15	60,277	904	61,181
16	61,181	918	62,099
17	62,099	931	63,031
18	63,031	945	63,976
19	63,976	960	64,936
20	64,936	974	65,910
21	65,910	989	66,898
22	66,898	1,003	67,902
23	67,902	1,019	68,920
24	68,920	1,034	69,954
25	69,954	1,049	71,003
26	71,003	1,065	72,069
27	72,069	1,081	73,150
28	73,150	1,097	74,247
29	74,247	1,114	75,360
30	75,360	1,130	76,491
31	76,491	1,147	77,638
32	77,638	1,165	78,803
33	78,803	1,182	79,985
34	79,985	1,200	81,185
35	81,185	1,218	82,402
36	82,402	1,236	83,638
37	83,638	1,255	84,893
38	84,893	1,273	86,166
39	86,166	1,292	87,459
40	87,459	1,312	88,771
41	88,771	1,332	90,102
42	90,102	1,352	91,454
43	91,454	1,372	92,826
44	92,826	1,392	94,218
45	94,218	1,413	95,631
46	95,631	1,434	97,066
47	97,066	1,456	98,522
48	98,522	1,478	1,00,000