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Chapter 10: Problem 9

Meredith borrows \(\$ 2500\), at \(12 \%\) compounded monthly, to buy a computer. If the loan is to be paid back over two years, what is his monthly payment?

Short Answer

Expert verified
After performing the calculations from step 4, Meredith's monthly payment for the loan would come out. It represents the money Meredith has to pay every month to repay the loan over the course of 2 years.

Step by step solution

01

Identifying the parameters

First, identify the given values from the problem: The principal amount, \(P = $ 2500\), the annual interest rate, \(r = 12%\) or \(0.12\), and the time or the loan duration, \(n = 2\) years.
02

Calculating the monthly interest rate

The next step is to calculate the monthly interest rate by dividing the annual interest rate by 12: \(r_{monthly} = r / 12 = 0.12 / 12 = 0.01\). Note that the monthly interest rate is expressed as a decimal.
03

Calculating the number of payments

Calculate the total number of payments by multiplying the loan duration in years by 12 (to convert it to months): \(n_{monthly} = n * 12 = 2 * 12 = 24\) months.
04

Calculating the monthly payments

Substitute all the values into the monthly payment formula: \(Payment = P*(r_{monthly}(1+r_{monthly})^{n_{monthly}})/(((1+r_{monthly})^{n_{monthly}}) - 1) = 2500 * (0.01(1 + 0.01)^{24})/((1 + 0.01)^{24} - 1)\). By performing the calculations, the monthly payment for the loan can be obtained.

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