Question

Michael took out a loan for $35,500 today. The interest rate on the loan was an APR of 12% compounded monthly. Michael pays annual payments of $9,800, how many years will it take before Michael pays back the loan?

	a.	4.56
	b.	5.03
	c.	6.25
	d.	8.10
	e.	5.15

Answer 1

Ans e. 5.15

EAR =	( 1 + r )^n - 1
	Compounded Monthly
EAR=	( 1 + 12%/12)^12 - 1
EAR=	12.68%

P =	Periodic Payments
r =	rate of interest
n =	no of periods
Annuity PV Factor =	P [ 1 - ( 1 + r )^-n ]
	r
35500 =	9800 * ( 1 - ((1 / (1 + 12.68%)^n)))
	12.68%
35500 / 9800 =	( 1 - ((1 / (1 + 12%/12)^n)))
	0.1268
35500 / 9800 * 0.1268 =	( 1 - ((1 / (1 + 12%/12)^n)))
0.459326530612245 =	( 1 - ((1 / (1 + 12%/12)^n)))
n =	5.15 years