Question

You have some extra cash this month and you are considering putting it toward your car loan. Your interest rate is 6.9 %​, your loan payments are $ 605 per​ month, and you have 36 months left on your loan. If you pay an additional $ 1 comma 300 with your next regular $ 605 payment​ (due in one​ month), how much will it reduce the amount of time left to pay off your​ loan? ​(Note: Be careful not to round any intermediate steps less than 6 decimal​ places.)

Answer 1

Since there is regular payments of $605 for 36 months remaining at rate of 6.9%, p.a.
its present value i.e. loan outstanding balance is as follows:
PMT	$                              605
Rate	0.575%	(6.9%/12)
NPER	36
PV	($19,622.854674)
	=PV(0.575%,36,605)
loan balance after next month regular payment, without additional $1,300
PMT	$                              605
Rate	0.575%
NPER	35
PV	($19,130.686088)
	=PV(0.575%,35,605)
loan balance after next month regular payment, with additional $1,300
	19,130.686088
	-1300
	17,830.686088
Now we will calculate time remaining to amortize that loan
PV	17,830.686088
Rate	0.575%
PMT	605
NPER	32.385875
	=NPER(0.575%,605,-17830.686088)
Time reduced to pay off the loan is (35 month- 32.385875 months)
	2.614125	months
	or 2.61 months	rounded