Question 1203861: 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
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! calculator used is at https://arachnoid.com/finance/
monthly compounding is assumed.
present value is 2000.
interest rate per time period is 18% per year / 12 = 1.5% per month.
number of time periods is 4 years * 12 = 48 months.
payments are made at the end of each time period.
future value is 0.
calculator says that the payment required at the end of each month is 58.75.
here's what it looks like.
Answer by ikleyn(52864)  (Show Source):
You can put this solution on YOUR website! .
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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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.
--------------------------------
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.
//////////////////////////////////////////
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.
|
|
|
