Question

(Compound interest with nonannual periods) After examining the various personal loan rates available to you, you find that you can borrow funds from a finance company at an APR of 11 percent compounded monthly or from a bank at an APR of 12 percent compounded annually. Which alternative is more attractive? a. If you borrow $100 from a finance company at an APR of 11 percent compounded monthly for 1 year, how much do you need to payoff the loan? $_____ (Round to the nearest cent.)

Answer 1

1.EAR=[(1+APR/m)^m]-1
where m=compounding periods

At an APR of 11 percent compounded monthly:

EAR=[(1+0.11/12)^12]-1

=11.57%(Approx)

At an APR of 12 percent compounded annually

EAR=[(1+0.12/1)^1]-1

=12%

Hence 11% compounded monthly is more attractive having lower EAR.

a.We use the formula:  
A=P(1+r/12)^12n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

A=100*(1+0.11/12)^(12*1)

=100*1.11571884

=$111.57(Approx)