/*! 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 6 Compute the simple interest for ... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Compute the simple interest for the specified period and the future value at the end of the period. Round all answers to the nearest cent. $$ \text { You borrow } \$ 6,000 \text { for } 5 \text { months at } 9 \% \text { per year. } $$

Short Answer

Expert verified
The simple interest for the specified period is \(225, and the future value at the end of the period is \)6,225.

Step by step solution

01

Convert the time period from months to years

We are given the time period in months, so we need to convert it to years as the interest rate is given per year. 5 months = \(\frac{5}{12}\) years
02

Calculate the simple interest

Use the simple interest formula: Simple Interest (SI) = Principal (P) × Rate (R) × Time (T) We are given: Principal (P) = $6,000 Rate (R) = 9% = 0.09 Time (T) = \(\frac{5}{12}\) years SI = \(6000 × 0.09 × \frac{5}{12}\)
03

Compute the simple interest value

Begin by calculating the product of 0.09 and 5. 0.09 × 5 = 0.45 Then, divide 0.45 by 12 to get the correct time period value. 0.45 ÷ 12 = 0.0375 Finally, multiply the principal amount by the above value to get the simple interest value. 6000 × 0.0375 = 225 Simple Interest (SI) = $225
04

Calculate the future value

Use the future value formula: Future Value (FV) = Principal (P) + Simple Interest (SI) FV = 6000 + 225
05

Compute the future value

Add the principal amount and the simple interest from the previous steps. 6000 + 225 = 6225 Future Value (FV) = $6,225 The simple interest for the specified period is \(225, and the future value at the end of the period is \)6,225.

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 91Ó°ÊÓ!

Key Concepts

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

Simple Interest Formula
Simple interest is a quick method of calculating the interest charge on a loan. This type of interest is calculated only on the original amount of money, known as the principal, which does not change over time. The simple interest formula is one of the foundational concepts in finance, critical for students and professionals alike.

The formula for calculating simple interest is expressed as:
\[ \text{Simple Interest (SI)} = \text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)} \]
With this straightforward formula, you can easily find out how much interest you'll owe over a certain period, provided the interest rate and the time frame stay constant. The resulting figure from this calculation represents the additional money that must be paid in addition to the original sum borrowed or invested.
Future Value Computation
Understanding the future value of a loan or investment is essential in planning and decision-making. The future value refers to the total amount of money an original principal will grow to over a period of time when compounded at a specific interest rate.

To compute the future value when dealing with simple interest, you can use the formula:
\[ \text{Future Value (FV)} = \text{Principal (P)} + \text{Simple Interest (SI)} \]
This calculation demonstrates the total money, including the original amount plus the interest earned after the specified time. It's a straightforward calculation that helps borrowers or investors understand exactly how much they will owe or have at the end of a particular period.
Principal Amount
The principal amount in simple interest calculations refers to the original sum of money loaned or invested, before any interest is added. It remains constant throughout the time period the interest is computed. In financial terminology, the principal amount is denoted by 'P'.

For a loan, it's the amount you borrow and are obliged to repay. For investments, it's the initial contribution you make that earns interest over time. When you see the term 'Principal' within equations or financial documents, it always means this base amount, not including any accrued interest.
Interest Rate Conversion
Interest rates are often presented annually, but loans and investments can span various periods - monthly, quarterly, or semi-annually. Therefore, converting the interest rate to match the time period of the investment or loan is a crucial step in interest calculations.

For instance, if a yearly interest rate is given and you need to calculate the interest for a number of months less than a year, you'd convert the annual rate into a monthly rate by dividing by 12 (the number of months in a year). Conversely, if you have a monthly rate but need to understand the annual impact, you would multiply by 12.

Here's a simple formula for converting annual interest rate to a monthly rate:
\[ \text{Monthly Rate (MR)} = \frac{\text{Annual Rate (AR)}}{12} \]
Accurate conversion ensures precise simple interest calculations, helping to avoid discrepancies in financial assessments.

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

My recent marketing idea, the Miracle Algae Growing Kit, has been remarkably successful, with monthly sales growing by \(6 \%\) every 6 months over the past 5 years. Assuming that I sold 100 kits the first month, how many kits did I sell in the first month of this year?

Meg's pension plan is an annuity with a guaranteed return of \(5 \%\) per year (compounded quarterly). She would like to retire with a pension of \(\$ 12,000\) per quarter for 25 years. If she works 45 years before retiring, how much money must she and her employer deposit each quarter? HINT [See Example 5.

Are based on the following chart, which shows monthly figures for Apple Inc. stock in \(2008 .^{14}\) Marked are the following points on the chart: $$\begin{array}{|c|c|c|c|c|c|} \hline \text { Jan. 2008 } & \text { Feb. 2008 } & \text { Mar. 2008 } & \text { Apr. 2008 } & \text { May 2008 } & \text { June 2008 } \\ \hline 180.05 & 125.48 & 122.25 & 153.08 & 183.45 & 185.64 \\ \hline \text { July 2008 } & \text { Aug. 2008 } & \text { Sep. 2008 } & \text { Oct. 2008 } & \text { Nov. 2008 } & \text { Dec. 2008 } \\ \hline 172.58 & 169.55 & 160.18 & 96.80 & 98.24 & 94.00 \\ \hline \end{array}$$ Suppose you bought Apple stock in January 2008 . If you later sold at one of the marked dates on the chart, which of those dates would have given you the largest annual return (assuming annual compounding), and what would that return have been?

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest \(0.001 \%\), as appropriate. Fees You are expecting a tax refund of 1,500 in 3 weeks. A tax preparer offers you a \(\$ 1,500\) loan for a fee of \(\$ 60\) to be repaid by your refund check when it arrives in 3 weeks. Thinking of the fee as interest, what simple interest rate would you be paying on this loan?

Determine the selling price, per \(\$ 1,000\) maturity value, of the bonds \(^{15}\) in Exercises 29-32. (Assume twice-yearly interest payments.) 10 year, \(4.875 \%\) bond, with a yield of \(4.880 \%\)

See all solutions

Recommended explanations on Math Textbooks

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.