Question

You have an outstanding student loan with required payments of $500 per month for the next four years. The interest rate on the loan is 8% APR.

You are considering making an extra payment of $200 today (that is, you will pay an extra $200 that you are not required to pay).

If you are required to continue to make payments of $500 per month until the loan is paid off, what is the amount of your final payment?

What rate of return (expressed as an APR with monthly compounding) have you earned on the $200?

Answer 1

	Dollars
Annuity Payment / Month	500
Time	48	months
APR	8%
Monthly Rate	0.67%
Total Loan Amount could be found out by Using Present Value Annuity Formula	=Annuity*[1-(1+r)^-n) / r]
	=500*[1-(1+0.67%)^-48 / 0.67%]
Solving the equation we get	=500*40.930
Total Loan Amount =	20465.00
	Loan Amortisation Schedule Normal						Loan Amortisation Schedule With $200 prepayment
	Month	Interest	Principal	Repayment	Balance at the end		Month	Interest	Principal	Repayment	Balance at the end
	1	136	364	500	20101		1	136	564	700	19901
	2	134	366	500	19735		2	133	367	500	19534
	3	132	368	500	19367		3	130	370	500	19164
	4	129	371	500	18996		4	128	372	500	18792
	5	127	373	500	18623		5	125	375	500	18417
	6	124	376	500	18247		6	123	377	500	18040
	7	122	378	500	17869		7	120	380	500	17660
	8	119	381	500	17488		8	118	382	500	17278
	9	117	383	500	17104		9	115	385	500	16893
	10	114	386	500	16718		10	113	387	500	16506
	11	111	389	500	16330		11	110	390	500	16116
	12	109	391	500	15939		12	107	393	500	15723
	13	106	394	500	15545		13	105	395	500	15328
	14	104	396	500	15149		14	102	398	500	14930
	15	101	399	500	14750		15	100	400	500	14530
	16	98	402	500	14348		16	97	403	500	14126
	17	96	404	500	13943		17	94	406	500	13721
	18	93	407	500	13536		18	91	409	500	13312
	19	90	410	500	13127		19	89	411	500	12901
	20	88	412	500	12714		20	86	414	500	12487
	21	85	415	500	12299		21	83	417	500	12070
	22	82	418	500	11881		22	80	420	500	11651
	23	79	421	500	11460		23	78	422	500	11228
	24	76	424	500	11037		24	75	425	500	10803
	25	74	426	500	10610		25	72	428	500	10375
	26	71	429	500	10181		26	69	431	500	9944
	27	68	432	500	9749		27	66	434	500	9511
	28	65	435	500	9314		28	63	437	500	9074
	29	62	438	500	8876		29	60	440	500	8634
	30	59	441	500	8435		30	58	442	500	8192
	31	56	444	500	7991		31	55	445	500	7747
	32	53	447	500	7545		32	52	448	500	7298
	33	50	450	500	7095		33	49	451	500	6847
	34	47	453	500	6642		34	46	454	500	6393
	35	44	456	500	6186		35	43	457	500	5935
	36	41	459	500	5728		36	40	460	500	5475
	37	38	462	500	5266		37	36	464	500	5011
	38	35	465	500	4801		38	33	467	500	4545
	39	32	468	500	4333		39	30	470	500	4075
	40	29	471	500	3862		40	27	473	500	3602
	41	26	474	500	3388		41	24	476	500	3126
	42	23	477	500	2910		42	21	479	500	2647
	43	19	481	500	2430		43	18	482	500	2165
	44	16	484	500	1946		44	14	486	500	1679
	45	13	487	500	1459		45	11	489	500	1190
	46	10	490	500	968		46	8	492	500	698
	47	6	494	500	475		47	5	495	500	203
	48	3	475	478	0		48	1	203	204	0
	Total	3513	20465	23978			Total	3440	20465	23904

2. Rate of Return : Should be calculated by understanding $74 as total savings on interest as return by pre-paying $200.00 in Month 1 thus RATE should be calculated by using excel formula i.e. =RATE(nper,,pv,[fv]); nper = 48 months; pv=200; fv= -274

=RATE(48,,200,-274) = 0.66% APR compounded monthly