Wednesday

August 20, 2014

August 20, 2014

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

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

- Business Math -
**MathMate**, Tuesday, June 21, 2011 at 4:29pmThe 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.

**Related Questions**

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

Business Finance - Cassandra is repaying an installment loan of $3500 with 20 ...

math - Cassandra is repaying an installment loan of 3,500 with 20 equal payments...

Math - Please check my answer thanks :) When repaing an installment loan of $3,...

Math - please help me thanks :) Paul needs to repay a loan(installment loan) of...

business math - financing furniture that costs $4200.00 with a two year ...

SOMEBODY HELP ME WITH MATH!!!!!! - A person wishes to borrow $20,000 and has the...

Finance - you have contacted a number of dearlerships to determine the best ...

Finance - you have contacted a number of dearlerships to determine the best ...

Finance - you have contacted a number of dearlerships to determine the best ...