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Chapter 8: Problem 6

In Exercises 1-12, the principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. a. Find how much money there will be in the account after the given number of years. (Assume 360 days in a year.) b. Find the interest earned. Round answers to the nearest cent. $$ \begin{array}{l|l|l|l|} \hline \text { 6. } \$ 2500 & 8 \% & \text { quarterly } & \text { 6 years } \end{array} $$

Short Answer

Expert verified
The total amount in the account after 6 years will be \$3709.84 and the interest earned will be \$1209.84.

Step by step solution

01

Computing Total Amount

We start by substituting the given values into the compound interest formula to calculate the total amount in the account after 6 years. Here, the principal P = $2500, annual interest rate r = 8% = 0.08 (converted to decimal), the number of compounding periods in a year n = 4 (since the money is compounded quarterly), and the number of years t = 6. This gives us: \( A = 2500(1 + 0.08/4) ^ {4*6} \)
02

Calculation

Now, we need to evaluate the expression. That results in \( A = 2500(1 + 0.02) ^ {24} = 2500(1.02) ^ {24} = \$3709.84. Everything is rounded to two decimal places, as per the problem's instructions. So, the total amount in the bank account after 6 years will be \$3709.84.
03

Computing Earned Interest

The earned interest can be determined by subtracting the initially deposited amount (principal) from the total amount in the account after 6 years. In other words, Interest earned = A - P = \$3709.84 - \$2500 = \$1209.84. Therefore, the interest earned over the 6 year period is \$1209.84.

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Key Concepts

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

Savings Account
A savings account is a type of bank account where you can store money securely while earning interest. It's a fundamental component of personal finance. When you deposit money into a savings account, the bank pays you interest as a reward for keeping your money with them. This means your money grows over time.
A savings account is suitable for short-term financial goals and emergency funds, due to:
  • Easy Access: Unlike fixed deposits, you can withdraw your money anytime.
  • Interest Earnings: Your money grows without extra work from you.
  • Security: Generally insured by financial institutions, safeguarding your funds.
Remember that savings accounts offer varying interest rates depending on the bank and current economic conditions. So, always explore different options before opening one.
Interest Calculation
Interest calculation is essential to understanding how your money grows in a savings account. Interest is the amount paid by the bank to the account holder for the privilege of holding their money. There are two main types of interest:
  • Simple Interest: Calculated on the original deposit, or principal, only.
  • Compound Interest: Calculated on the initial principal and also on the accumulated interest of previous periods.
The calculation involves basic formulas. For compound interest, which is more common in savings accounts, the compound interest formula is used to find out how much interest you will earn over a period. This understanding helps in making informed decisions about where to put your money.
Compound Interest Formula
The compound interest formula is a key tool in personal finance. It helps calculate the total amount in a savings account including the interest earned, over a specified period. The formula is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
  • \(A\) = the future value of the investment/loan, including interest.
  • \(P\) = the principal investment amount (initial deposit or loan amount).
  • \(r\) = the annual interest rate (decimal).
  • \(n\) = number of times the interest is compounded per year.
  • \(t\) = the number of years the money is invested for.
This formula allows you to compute the exact amount to expect after a certain number of years. It's especially useful for planning long-term savings and understanding how different factors affect the growth of your investment.
Financial Literacy
Financial literacy involves understanding fundamental financial concepts, like those mentioned above, to make informed and effective decisions about managing personal finances. It encompasses:
  • Savings strategies and understanding different savings accounts.
  • Investment principles and the importance of growing your wealth.
  • Budgeting and managing expenses wisely.
  • Comprehending interest calculations to maximize earnings on deposits.
Being financially literate means being equipped with the knowledge to handle money wisely, enabling you to make better financial choices and secure your future. Learning how interest works, especially compound interest, is a critical part of this journey.

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Most popular questions from this chapter

If an investor sees that the return from dividends for a stock is lower than the return for a no-risk bank account, should the stock be sold and the money placed in the bank account? Explain your answer.

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