posted by Sandy

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?

1. MathMate

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.

## Similar Questions

1. ### Math

Please check my answer thanks :) When repaing an installment loan of \$3,500 with 20 equal monthly payments of \$196 each , the apr of the loan is my answer is 13.5 %
2. ### Math

please help me thanks :) Paul needs to repay a loan(installment loan) of \$3,500 with 20 equal monthly payments of \$196 each. What is the APR of the laon?
3. ### math

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?
4. ### business math

financing furniture that costs \$4200.00 with a two year installment loan. The loan requires a 12% down payment and 24 equal monthly payments of \$195.00. According to this information, what would be the finance charge on the loan?
5. ### math

Cassandra is repaying an installment loan of 3,500 with 20 equal payments of 196.00 each.What is the annual percentage rate of the loan?
6. ### SOMEBODY HELP ME WITH MATH!!!!!!

A person wishes to borrow \$20,000 and has the following options. One lending source offers the loan for 24 monthly payments at an annual percentage rate of 14%. The second source offers the loan for 18 monthly payments at an annual …
7. ### Business Finance

Cassandra is repaying an installment loan of \$3500 with 20 equal monthly payments of \$196 each. What is the annual percentage rate of the loan?
8. ### Corporate Finance

You have just taken a 30-year mortgage loan for \$200,000. The annual percentage rate on the loan is 8%, and payments will be made monthly. Estimate your monthly payments.
9. ### Business math

find the annual percentage rate on a loan of \$1,500 for 18months if the loan requires \$190 interest and is repaid monthly.
10. ### math

You purchase a hot tub costing \$4,600 by taking out a 13% add-on interest installment loan. The loan requires a 15% down payment and equal monthly payments for 4 years. How much are your monthly payments?

More Similar Questions