/*! 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 1 A friend lends you \(\$ 200\) fo... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 1

A friend lends you \(\$ 200\) for a week, which you agree to repay with \(5 \%\) one-time interest. How much will you have to repay?

Short Answer

Expert verified
You will have to repay $210.

Step by step solution

01

Understanding the Problem

You borrowed $200 from your friend and agreed to a one-time interest rate of 5%. We need to calculate the total amount to be repaid, which includes the original amount plus interest.
02

Calculating the Interest

To find the interest, use the formula for simple interest: \( \, Interest = Principal \times Rate \, \). Here, the principal is \\(200 and the rate is 5% or 0.05. So, the interest is \( \\)200 \times 0.05 = \$10 \).
03

Calculating the Total Repayment

The total amount to be repaid is the principal plus the interest. Add the interest amount to the original loan amount: \( \\(200 + \\)10 = \$210 \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Loan Repayment
When you borrow money from someone or an institution, it's important to understand what loan repayment means. Repayment refers to paying back the borrowed amount, which is often called the principal, along with any additional costs like interest. In most scenarios, you'll negotiate a repayment plan:
  • This plan can be weekly, monthly, or at another agreed-upon interval.
  • Repayment terms vary depending on the lender and the type of loan.
In our example where you borrowed \(\\(200\), the repayment consists of the principal and the interest, which we calculated to be \(\\)10\). Hence, the total amount you'll pay back is \(\$210\). Understanding how loan repayment works will help you manage your finances better and avoid unexpected financial burden.
Interest Rate
The interest rate is a key part of financial agreements involving loans. It is the percentage charged on the principal amount borrowed. Whenever you borrow money, the lender charges interest, which is their way of earning profit or compensation for the risk of lending funds.
Here's how to think about it:
  • An interest rate can be a one-time charge, like in our example, or it can accrue over time, such as annually.
  • The rate is expressed as a percentage of the principal.
  • A higher interest rate means you'll pay more over the life of the loan.
In our exercise, the interest rate was 5%, calculated on a principal of \(\\(200\). So, the interest to be paid is \(\\)10\). Understanding interest rates is crucial when comparing loan options and making smart borrowing decisions.
Financial Literacy
Financial literacy represents the understanding of financial principles and concepts. It enables individuals to make informed decisions regarding their money. Being financially literate involves:
  • Knowing how to calculate interest and understand loan terms.
  • Being aware of how interest rates affect the total repayment.
  • Understanding terms like principal, interest, and repayment schedule.
Knowledge in these areas helps individuals in making better budgeting, saving, and investment decisions.
In our example, the awareness of a 5% interest resulted in knowing the exact repayment amount, preventing surprises. Thus, financial literacy is essential in navigating the often complex world of personal finance and lending.
Mathematics Education
Mathematics education provides invaluable skills for calculating financial problems. Understanding and solving real-world problems, like calculating loan repayment, often requires applying mathematical concepts.
  • Basic arithmetic is used to compute totals, differences, and percentages.
  • Formulas, such as that for simple interest, help simplify complex calculations.
  • Math education strengthens critical thinking and problem-solving skills.
In the example provided, we used the simple interest formula: \( \text{Interest} = \text{Principal} \times \text{Rate} \) to find the interest amount and then added it to the principal. This technique showcases how practical math skills are in everyday financial decisions. Mathematical literacy empowers students to approach and overcome financial challenges with confidence.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Imagine a certain savings account started out with a balance of \(\$ 5250.00\) on day-one, and today has a current balance of \(\$ 5780.23\) a. Exactly how much more money does the account have today, compared with day- one? b. Rounding to the nearest tenth of a percent: By what percentage amount has the account balance grown? c. If instead, the bank balance today was exactly double the starting balance, then by what exact percentage amount would the bank balance have grown? d. If the bank balance today had instead grown by \(15.5 \%\) since day-one, then what would be the exact amount of today's balance?

You deposit \(\$ 1,000\) into an account earning \(5.75 \%\) APR compounded continuously. a. How much will you have in the account in 15 years? b. How much total interest will you earn? c. What percent of the balance is interest?

You wish to have \(\$ 3,000\) in 2 years to buy a fancy new stereo system. How much should you deposit each quarter into an account paying \(6.5 \%\) APR compounded quarterly?

Suppose another mortgage lender offers you a fixed-rate 15 -year mortgage at \(2.95 \%\) APR. You have \(\$ 20,000\) saved as a down payment, and you can afford a maximum mortgage payment of \(\$ 950\) per month. You are interested in a certain house for sale, with firm selling price of \(\$ 200,000\). a. Find the monthly payment for this house. Can you afford it, under the terms of this lender? b. (Challenge): Suppose this same lender offers to increase the APR by only \(0.05 \%,\) for each additional year added to the loan period beyond 15 years (so that a 16-year loan would have \(3.00 \%\) APR, and a 17-year loan would have \(3.05 \%\) APR, and so on ), up to a maximum loan period of 25 years. Given these terms, does any combination of APR and loan period exist that would let you afford the house? If so, state the minimum number of additional years needed, the total resulting loan period, the resulting APR, and the resulting monthly payment.

Determine which formula from sections \(2.2-2.4\) to use and solve the problem. Paul wants to buy a new car. Rather than take out a loan, he decides to save \(\$ 200\) a month in an account earning \(3.5 \%\) APR compounded monthly. How much will he have saved up after 3 years?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.