Determining the Interest rate based on payments

HomeworkDuring class today as we were working the problem of the day, several people proposed possible interest rates to go with the interest paid by Henrí in paying off his loan.

Using a calculator similar to the one we used on Friday, it is possible to determine the interest rate.

Interest rate calculation from calculator.net. The formula for this calculation isn't exactly simple.
Interest rate calculation from calculator.net. The formula for this calculation isn’t exactly simple.

I like this calculator, but I’m sure there are plenty more to choose from. Plugging in our example of $274/month for 36 months returns an interest rate of 6.05% for a total interest cost of $864.00. Several suggested that you could simply divide \frac{864}{9000}=9.6%?

Why does an interest rate of 6.05% per year end up with a total cost of 9.6%? Why would it not be .0605\cdot 3=18%?

Ponder those questions for next time.

Remember to take a look at the rest of the exploration for 16.3 (page 453, green book) and get started on the homework, but the homework won’t be due until Thursday. I do expect you to complete the exploration before class on Wednesday.

Feeling adventurous? Remember the equation I mentioned in the last post about this topic?

R=\frac{P\cdot i}{1-{{(1+i)}^{-n}}}

You can use a function on the Nspire handheld to solve that equation for i to find the interest rate. On the handheld, you’d input something like this:

Using nSolve on the Nspire handheld, you can solve the equation to find the interest rate. How could you modify the input to solve for the number of months as in problem 13 from the 16.1 homework?
Using nSolve on the Nspire handheld, you can solve the equation to find the interest rate. How could you modify the input to solve for the number of months as in problem 13 from the 16.1 homework?

Note that the variable you solve for is the interest per month. To get the equivalent annual rate, you must multiply by 12.

 

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