/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 17 We will discuss engineering econ... [FREE SOLUTION] | 91影视

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Chapter 14: Problem 17

We will discuss engineering economics in Chapter \(20 .\) Using Excel, create a table that can be used to look up monthly payments on a car loan for a period of five years. The monthly payments are calculated from $$ A=P\left[\frac{\left(\frac{i}{1200}\right)\left(1+\frac{i}{1200}\right)^{60}}{\left(1+\frac{i}{1200}\right)^{60}-1}\right] $$ where \(A=\) monthly payments in dollars \(P=\) the loan in dollars \(i=\) interest rate, e.g., \(7,7.5, \ldots, 9\) \begin{tabular}{|l|l|l|l|l|l|} \hline \multicolumn{7}{|c|}{ Interest Rate } \\ \cline { 2 - 6 } Loan & 7 & \(7.5\) & 8 & \(8.5\) & 9 \\ \hline 10,000 & & & & & \\ \hline 15,000 & & & & & \\ \hline 20,000 & & & & & \\ \hline 25,000 & & & & & \\ \hline \end{tabular}

Short Answer

Expert verified
The detailed monthly payment amounts for different loan amounts and interest rates can be calculated using the given formula on Excel.

Step by step solution

01

Understand the Loan Payment Formula

Understand the formula for calculating monthly payments: \( A=P \left[ \frac { \left( \frac{i}{1200} \right) \left(1+\frac{i}{1200} \right)^{60} }{ \left(1+\frac{i}{1200} \right)^{60}-1 } \right] \), where A signifies the monthly payments, P is the loan amount in dollars and i represents the interest rate.
02

Setting Up Excel

Open Excel. Set up the columns and rows to match the given table, where columns represent different interest rates and rows represent different loan amounts.
03

Apply Formula

In the cell where you want to start the calculation (for example B2 if starting from the $10,000 loan with 7% interest), type the formula: =10000 * (((7/1200) * (1 + 7/1200)^60) / ((1 + 7/1200)^60 - 1)). This will calculate the monthly payment for a loan of $10,000 at 7% interest.
04

Filling the Table

To fill the table, simply repeat step 3 for each cell, replacing the interest rate and loan amount as appropriate.
05

Review Results

Check the results and notice how varying interest rates and loan amounts affect the monthly payments.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Loan Payment Formula
The loan payment formula is essential in engineering economics, particularly when dealing with annuities like car loans. It helps calculate the consistent payment needed over a specified period for a loan. The formula is \[ A = P \left[ \frac{\left(\frac{i}{1200}\right) \left(1+\frac{i}{1200}\right)^{60}}{\left(1+\frac{i}{1200}\right)^{60} - 1} \right] \], where:
  • A is the monthly payment amount.
  • P is the loan amount in dollars.
  • i is the annual interest rate expressed as a percentage.
This formula assumes that the payments are made monthly and that the interest rate is compounded monthly over the loan's term. The value 60 in the formula corresponds to the total number of monthly payments for a five-year period.
Monthly Payments
Monthly payments represent how much you need to pay each month over the course of a loan. This amount is drawn from the loan payment formula and varies depending on the principal amount of the loan, the interest rate, and the term of the loan.
For example, with a $10,000 loan at a 7% interest rate, according to our formula, you'll find the exact figure you'll need to pay every month. This consistency in payments makes budgeting easier and helps you manage your finances effectively. The monthly payment thus reflects both principal repayment and interest.
Interest Rate
The interest rate is a critical factor in loan calculations. It impacts the cost of borrowing and how much you'll pay in total for a loan. In the loan payment formula, the interest rate \(i\) is divided by 1200 to convert the annual rate into a monthly rate.
  • An interest rate of 7% becomes \( \frac{7}{1200} \) as the monthly rate.
  • The formula uses this to calculate the compounded interest over the loan's term.
Interest rates can vary over time or depending on your credit score, influencing your monthly payment and total cost of the loan. It's essential to compare rates and understand their long-term impact on your finances.
Excel Calculations
Excel is a powerful tool for performing these calculations effortlessly. By setting up a spreadsheet to replicate the loan payment table, you can quickly determine monthly payments across different scenarios.
Use Excel formulas to directly apply the loan payment formula to various cells, automating repetitive calculations. For instance, in a cell, you might input \( =P \times \left( \frac{(i/1200) \times (1 + i/1200)^{60}}{(1 + i/1200)^{60} - 1} \right) \), replacing \(P\) and \(i\) with the specific loan amount and interest rate for each calculation.
Excel's fill-down feature can populate the rest of the table quickly once you've calculated the first item, thus saving time and reducing errors.

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Most popular questions from this chapter

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