You’ve borrowed $1,766.14 and agreed to pay back the loan with monthly payments of $120.

You’ve borrowed $1,766.14 and agreed to pay back the loan with monthly payments of $120. Assume the interest rate is 12% stated as an APR.

a. How long will it take you to pay back the loan?
 
b. What is the effective annual rate on the loan?
 

Explanation
Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

a.
1.1726

PV	=	C((1 / r) – {1 / [r(1 + r)t]})
$4,248.68	=	$120 × [[1 / (0.12 / 12)] – (1 / {(0.12 / 12)[1 + (0.12 / 12)]t})]
21.2434	=	100.00 – 1 / [.0100(1.0100t)]
1 / [[.0100(1.0100t)]	=	85.2821
0.0100(1.0100t)	=	0.0117
1.0100t	=	1.1726
t × ln1.0100	=	ln1.1726
t	=	16 months

b.

EAR	=	[1 + (APR / t)]t – 1
	=	[1 + (.12 / 12)]12 – 1
	=	0.1268, or 12.68%

Calculator computations:

Enter

12 / 12

1,766.14

–120

N

I/Y

PV

PMT

FV

Solve for

16

On some calculators, you can compute the effective annual rate using the "ICONV" function:
 

NOM	=	12
C/Y	=	12
CPT EFF	=	12.68