Posted by **Sandy** on Sunday, June 19, 2011 at 6:44pm.

Cassandra is repaying an installment loan of $3,500 with 20 equal monthly

payments of $196 each. what is the annual percentage rate of the loan?

- Business Math -
**MathMate**, Tuesday, June 21, 2011 at 4:29pm
The standard formula for installment amount A, for n periods with interest per period i, and present value (principal) P is

A=P((1+i)^n)i/((1+i)^n-1)

where

n=20,

A=196

P=3500

substitute to get

196=3500i(1+i)^20/((1+i)^20-1)

I do not believe there is an explicit formula to solve for i, so we can solve it by trial and error or by iteration.

Rearrange to give

f(i)=196-3500i(1+i)^20/((1+i)^20-1)

and we look for i that makes f(i)=0.

Make a table:

f(0.005)=11.67

f(0.01)=2.04

f(0.015)=-7.86

Interpolating, we try

f(0.011)=0.0878

f(0.0111)=-0.1086

So give a final try of

f(0.011045)=-0.0005...

The interest per period is 1.1045%

Annual interest

=1.1045*12=13.254% approx.

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