Question

You have an outstanding student loan with required payments of $ 600 per month for the next four years. The interest rate on the loan is 8% APR​ (monthly). You are considering making an extra payment of $150 today​ (that is, you will pay an extra $150 that you are not required to​ pay). If you are required to continue to make payments of $600 per month until the loan is paid​ off, what is the amount of your final​ payment? What effective rate of return​ (expressed as an APR with monthly​ compounding) have you earned on the $150​?

Answer 1

A	B	C	D	E	F	G	H
2
3		Monthly Payments	$600
4		Annual interest rate	8%
5		Monthly interest rate	0.67%
6		Period in years	4		0.083
7		Period in month	48
8
9		The outstanding amount of loan will be the present value of all the payments.
10
11		Outstanding amount of loan	=Monthly amount*Present value factor
12			=$600*(P/A,0.67%,48)
13			$24,577.15	=D3*PV(D5,D7,-1,0)
14
15		Extra amount Paid today	$150
16		Let the amount of the final payment is X,
17		then the present value of all the payments should be equal to the present value
18		of the loan calculated above i.e.
19		150+600*(P/A,0.67%,47)+X*(P/F,0.67%,48) = $24,577.15
20
21		(P/A,0.67%,47)	40.23
22		(P/F,0.67%,48)	0.73
23
24		150+600*(P/A,0.67%,47)+X*(P/F,0.67%,48) = $24,577.15
25		or
26		150+600*40.23+X*0.73 = $24,577.15
27		or
28		150+24141+0.73*X = $24,577.15
29		or
30		X	$391.98
31
32		Hence Amount of final payment	$391.98
33
34		Amount Saved	$208.02
35		Extra amount deposited	$150
36		Period	4	Years
37		Thus extra amount of $150 deposited today resulted in saving of $208.02 after 4 years
38		Let interest rate be i,
39		Thus,
40		150*(1+i)^4 = 208.02
41		or
42		i	=(208.02/150)^(1/4)-1
43			8.52%
44
45		Hence interest rate earned on $150 is	8.52%
46