Question

you have an outstanding student loan with required payments of

$550

per month for the next four years. The interest rate on the loan is

10%

APR. You are considering making an extra payment of

$100

today? (that is, you will pay an extra

$100

that you are not required to? pay).

a. If you are required to continue to make payments of

$550

per month until the loan is paid? off, what is the amount of your final? payment???

b. What effective rate of return? (expressed as an APR with monthly? compounding) have you earned on the

$100??

c. Now that you realize your best investment is to prepay your student? loan, you decide to prepay as much as you can each month. Looking at your? budget, you can afford to pay an extra

$250

per month in addition to your required monthly payments of

$550?,

or

$800

in total each month. How long will it take you to pay off the? loan?

Answer 1

	Interest rate=10% APR
	Monthly interest rate=(10/12)%	0.008333
	Number of instalments=4*12	48
	Monthly payment	$550
	Loan amount	$21,685.49	(Using PV function of excel with Rate=(10/12)%,Nper=48, Pmt=-550)
	If we pay $100 today, loan amount	$21,585.49	(21685-100)
	N	A	B	C=A*0.008333	D=B-C	E=A-D
	Month	Beginning Balance	Payment	Interest	Principal	Ending Balance
	1	$21,585.49	$550	$179.88	$370.12	$21,215.37
	2	$21,215.37	$550	$176.79	$373.21	$20,842.16
	3	$20,842.16	$550	$173.68	$376.32	$20,465.85
	4	$20,465.85	$550	$170.55	$379.45	$20,086.40
	5	$20,086.40	$550	$167.39	$382.61	$19,703.78
	6	$19,703.78	$550	$164.20	$385.80	$19,317.98
	7	$19,317.98	$550	$160.98	$389.02	$18,928.96
	8	$18,928.96	$550	$157.74	$392.26	$18,536.71
	9	$18,536.71	$550	$154.47	$395.53	$18,141.18
	10	$18,141.18	$550	$151.18	$398.82	$17,742.36
	11	$17,742.36	$550	$147.85	$402.15	$17,340.21
	12	$17,340.21	$550	$144.50	$405.50	$16,934.71
	13	$16,934.71	$550	$141.12	$408.88	$16,525.83
	14	$16,525.83	$550	$137.72	$412.28	$16,113.55
	15	$16,113.55	$550	$134.28	$415.72	$15,697.83
	16	$15,697.83	$550	$130.82	$419.18	$15,278.64
	17	$15,278.64	$550	$127.32	$422.68	$14,855.96
	18	$14,855.96	$550	$123.80	$426.20	$14,429.76
	19	$14,429.76	$550	$120.25	$429.75	$14,000.01
	20	$14,000.01	$550	$116.67	$433.33	$13,566.68
	21	$13,566.68	$550	$113.06	$436.94	$13,129.73
	22	$13,129.73	$550	$109.41	$440.59	$12,689.15
	23	$12,689.15	$550	$105.74	$444.26	$12,244.89
	24	$12,244.89	$550	$102.04	$447.96	$11,796.93
	25	$11,796.93	$550	$98.31	$451.69	$11,345.24
	26	$11,345.24	$550	$94.54	$455.46	$10,889.78
	27	$10,889.78	$550	$90.75	$459.25	$10,430.53
	28	$10,430.53	$550	$86.92	$463.08	$9,967.45
	29	$9,967.45	$550	$83.06	$466.94	$9,500.51
	30	$9,500.51	$550	$79.17	$470.83	$9,029.69
	31	$9,029.69	$550	$75.25	$474.75	$8,554.93
	32	$8,554.93	$550	$71.29	$478.71	$8,076.22
	33	$8,076.22	$550	$67.30	$482.70	$7,593.53
	34	$7,593.53	$550	$63.28	$486.72	$7,106.81
	35	$7,106.81	$550	$59.22	$490.78	$6,616.03
	36	$6,616.03	$550	$55.13	$494.87	$6,121.16
	37	$6,121.16	$550	$51.01	$498.99	$5,622.17
	38	$5,622.17	$550	$46.85	$503.15	$5,119.02
	39	$5,119.02	$550	$42.66	$507.34	$4,611.68
	40	$4,611.68	$550	$38.43	$511.57	$4,100.11
	41	$4,100.11	$550	$34.17	$515.83	$3,584.28
	42	$3,584.28	$550	$29.87	$520.13	$3,064.15
	43	$3,064.15	$550	$25.53	$524.47	$2,539.68
	44	$2,539.68	$550	$21.16	$528.84	$2,010.85
	45	$2,010.85	$550	$16.76	$533.24	$1,477.60
	46	$1,477.60	$550	$12.31	$537.69	$939.92
	47	$939.92	$550	$7.83	$542.17	$397.75
	48	$397.75	$401.07	$3.31	$397.76	($0.00)
a	Amount of final payment	$401.07
	Saving in final payment	$148.93	(550-401.07)
b	Monthly return =R
	100*((1+R)^48)=148.93
	((1+R)^48)=148.93/100=1.4893
	1+R=(1.4893^(1/48))=	1.00833257
	R=	0.00833257
	Monthly return =R=	0.833257%
	APR=(0.833257*12)%=	10%
c	Loan Amount	$21,585.49
	Monthly interest =(10/12)%
	Monthly payment	$800
	Number of months required to pay off the loan	30.69084149	(Using Nper function of excel with Rate=(10/12)%, Pmt=-800, PV=21585.49)
	Number of months required to pay off the loan	31
	N	A	B	C=A*0.008333	D=B-C	E=A-D
	Month	Beginning Balance	Payment	Interest	Principal	Ending Balance
	1	$21,585.49	$800	$179.88	$620.12	$20,965.37
	2	$20,965.37	$800	$174.71	$625.29	$20,340.08
	3	$20,340.08	$800	$169.50	$630.50	$19,709.58
	4	$19,709.58	$800	$164.25	$635.75	$19,073.83
	5	$19,073.83	$800	$158.95	$641.05	$18,432.78
	6	$18,432.78	$800	$153.61	$646.39	$17,786.38
	7	$17,786.38	$800	$148.22	$651.78	$17,134.60
	8	$17,134.60	$800	$142.79	$657.21	$16,477.39
	9	$16,477.39	$800	$137.31	$662.69	$15,814.70
	10	$15,814.70	$800	$131.79	$668.21	$15,146.49
	11	$15,146.49	$800	$126.22	$673.78	$14,472.71
	12	$14,472.71	$800	$120.61	$679.39	$13,793.32
	13	$13,793.32	$800	$114.94	$685.06	$13,108.26
	14	$13,108.26	$800	$109.24	$690.76	$12,417.50
	15	$12,417.50	$800	$103.48	$696.52	$11,720.98
	16	$11,720.98	$800	$97.67	$702.33	$11,018.65
	17	$11,018.65	$800	$91.82	$708.18	$10,310.47
	18	$10,310.47	$800	$85.92	$714.08	$9,596.39
	19	$9,596.39	$800	$79.97	$720.03	$8,876.36
	20	$8,876.36	$800	$73.97	$726.03	$8,150.33
	21	$8,150.33	$800	$67.92	$732.08	$7,418.25
	22	$7,418.25	$800	$61.82	$738.18	$6,680.07
	23	$6,680.07	$800	$55.67	$744.33	$5,935.74
	24	$5,935.74	$800	$49.46	$750.54	$5,185.20
	25	$5,185.20	$800	$43.21	$756.79	$4,428.41
	26	$4,428.41	$800	$36.90	$763.10	$3,665.32
	27	$3,665.32	$800	$30.54	$769.46	$2,895.86
	28	$2,895.86	$800	$24.13	$775.87	$2,119.99
	29	$2,119.99	$800	$17.67	$782.33	$1,337.66
	30	$1,337.66	$800	$11.15	$788.85	$548.81
	31	$548.81	$553	$4.57	$548.81	$0.00