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Chapter 3: Problem 3

Sally deposits \(\$ 4,000\) in a certificate of deposit that pays 6\(\frac{3}{4} \%\) simple interest. What is her balance after one year?

Short Answer

Expert verified
Sally's balance after one year will be $\$4,270.

Step by step solution

01

Calculate the interest rate as a decimal

The interest rate is given as a fraction: 6 and 3/4 percent. First, add 6 to 3/4 to get the percentage in a decimal format: 6.75 . Then, divide this by 100 to convert it to a decimal: 0.0675
02

Calculate the interest

Apply the equation I = Prt , where I is the interest, P is the principal (\$4,000), r is the interest rate (0.0675), and t is the time (1 year). This yields the result I = 4000 * 0.0675 * 1 = $270.
03

Calculate the balance after one year

Add the interest to the initial deposit: \$4,000 + \$270 = \$4,270

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Key Concepts

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

Understanding Certificates of Deposit
A Certificate of Deposit (CD) is a financial product commonly offered by banks. It's a type of savings account with a set interest rate and fixed maturity date. When you open a CD, you deposit money for a specified term during which you can鈥檛 access the funds without a penalty. In return, the bank pays you interest on your deposit.
  • Fixed Term: CD terms can range from a few months to several years. You agree to leave your money in the account until the term ends.
  • Interest Rates: CDs often offer a predictable and typically higher interest rate than regular savings accounts, making them an attractive option for those looking to earn more from their savings.
  • Security: Your investment is secure as long as it remains within the limits of FDIC insurance in the United States.
After the specified term, you receive your initial deposit plus the accrued interest. Understanding how interest is calculated, such as simple interest, is crucial when investing in CDs.
Interest Rate Conversion Explained
Converting interest rates into a usable format is an important step in financial calculations. Rates are often presented as percentages, but we need them as decimals for mathematical equations.Let鈥檚 break down the process:
  • Convert fractions to decimals: If an interest rate includes a fraction, convert it into a decimal. For example, 6 3/4% becomes 6.75%.
  • Change percentage to decimal: Divide the percentage by 100. So, 6.75% becomes 0.0675 in decimal form.
  • Use in calculations: The decimal form allows integration into formulas, like calculating simple interest using the formula \(I = Prt\).
This method ensures accuracy in calculations involving interest-bearing instruments like CDs.
Financial Algebra Simplified
Financial algebra involves using mathematical operations and formulas to solve financial problems, helping calculate values like interest or future balances.In the context of simple interest:
  • Formula: Simple interest is calculated with \(I = Prt\), where \(I\) is the interest earned, \(P\) is the principal amount, \(r\) is the interest rate in decimal form, and \(t\) is the time in years.
  • Understanding Units: Each part of the formula requires specific units (money in dollars, time in years) to maintain consistency.
  • Application: Once you've calculated the interest, you can determine the total balance by adding it to the initial principal.
Financial algebra is an invaluable tool in personal finance, enabling you to make informed decisions about various financial products and understand their benefits. It bridges the gap between theoretical percentages and real-world applications, such as understanding how a CD can grow your savings over time.

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Most popular questions from this chapter

Anna has a checking account at Garden City Bank. Her balance at the beginning of February was \(\$ 5,195.65 .\) During the month, she made deposits totaling \(\$ 6,873.22,\) wrote checks totaling \(c\) dollars, was charged a maintenance fee of \(\$ 15,\) and earned \(\$ 6.05\) in interest. Her balance at the end of the month was \(\$ 4,200.00 .\) What is the value of \(c ?\)

Linda's savings account has fallen below the \(\$ 1,000\) minimum balance required to receive interest. It is currently \(\$ 871.43 .\) The monthly fee charged by the bank for falling below the minimum is \(x\) dollars. Express algebraically how you compute the number of months it will take Linda's account to reach a zero balance if she makes no deposits. Explain. If \(x=9,\) how many months will it take?

Suni needs to repay her school loan in 4 years. How much must she semiannually deposit into an account that pays 3.9\(\%\) interest, compounded semiannually, to have \(\$ 100,000\) to repay the loan?

Janine is 21 years old. She opens an account that pays 4.4\(\%\) interest, compounded monthly. She sets a goal of saving \(\$ 10,000\) by the time she is 24 years old. How much must she deposit each month?

An elite private college receives large donations from successful alumni. The account that holds these donations has \(\$ 955,000,000\) currently. a. How much would the account earn in one year of simple interest at a rate of 5.33\(\%\) ? b. How much would the account earn in one year at 5.33\(\%\) if the interest was compounded daily? Round to the nearest cent. c. How much more interest is earned by compounded daily as compared to simple interest? d. If the money is used to pay full scholarships, and the price of tuition is \(\$ 61,000\) per year to attend, how many more students can receive full four- year scholarships if the interest was compounded daily rather than using simple interest?
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