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you have 2,000 on a credit card that charge a 18% interest rate if you want to pay off the credit card in 4 years.
how much will you need to pay each month
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This my solution goes second after the solution by @Theo.
@Theo used an online calculator in his solution.
Since this web-site is to teach Math, the expected solution should be mathematical.
So, I present here a standard mathematical solution.
Calculator can be used as a secondary tool for verification.
Then the sequence of steps would be normally educative.
This is a standard problem on amortization debt (same as paying back for a loan).
Use the standard formula for the monthly payment for a loan
M =
where P is the loan amount; r = = 0.015 is the effective interest rate per month;
n is the number of payments (same as the number of months); M is the monthly payment.
In this problem P = $2000; r = = 0.015.
(We are lucky in this case, since we have a precise decimal value for the effective interest rate).
Substitute these values into the formula and get for monthly payment
M = = $58.75.
ANSWER. The monthly payment is $58.75.
Compare it with the @Theo answer of $58.75.
It coincide cent-to-cent with my answer.
Solved mathematically.
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In such calculations, it is important to avoid intermediate rounding.
Rounding can be done at the end, only.
Intermediate rounding is PROHIBITED, since it leads to wrong answer.
Also, a calculator should provide the necessary precision.
I use MS Excel in my computer. It works with 15 decimals in mantissa
and provides the necessary precision.
I simply copy-paste my numerical formula into Excel spreadsheet and get the answer in one click.
Many standard online calculators provide the necessary precision.
You may use, for example, these free-of-charge online calculators
https://www.calculatorsoup.com/calculators/financial/loan-calculator.php
https://www.calculator.net/payment-calculator.html
They are reliable, have convenient user-friendly interface, have complete instructions and descriptions,
provide the necessary precision and were checked million times. You may use them to check my/your calculations.
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There is another (= one more) reason why I produced and placed my solution here.
@Theo' posts used visual plots to support his solutions.
These plots were integral inseparable part of his solutions.
But some time ago, Theo left this forum and stopped supporting web-site with his plots.
As a result, you see now some colored spots in his posts, where his plots should be.
Due to this reason, @Theo's posts lost their educational meaning and value.
Therefore, I create my posts with my own mathematical solutions
to replace @Theo' solutions and provide meaningful mathematical content.
