The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Answer parts (a) and (b).
| Principal | Rate | Compounded | Time |
| --------- | ------- | ---------- | ------- |
| $7000 | 0.6 % | quarterly | 5 years |
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a. Find how much money there will be in the account after the given number of years.
The amount of money in the account after 5 years is $7213.02.
(Round to the nearest cent as needed
b. Find the interest earned.
The amount of interest earned is $ $\square$
(Round to the nearest cent as needed.)
Answer (2)
Calculate the interest earned by subtracting the principal from the final amount.
The amount after 5 years is $7213.02 and the principal is $7000.
Perform the subtraction: $7213.02 - $7000 = $213.02.
The interest earned is $\boxed{ 213.02} .
Explanation
Understanding the Problem We are given the principal amount, the interest rate, the compounding period, and the time. We are also given the amount of money in the account after 5 years, which is $7213.02. We need to find the interest earned.
Finding the Interest Earned To find the interest earned, we subtract the principal amount from the amount after 5 years. That is: I n t eres t = A m o u n t a f t er 5 ye a rs − P r in c i p a l
Substituting the Values Substituting the given values, we have: Interest = $7213.02 - $7000
Calculating the Interest Performing the subtraction, we get: Interest = $213.02
Examples
Understanding compound interest is crucial for making informed financial decisions. For example, knowing how interest accrues can help you decide between different savings accounts or investment options. Suppose you want to save for a down payment on a house. By understanding compound interest, you can estimate how much your initial investment will grow over time, helping you plan your savings strategy more effectively. This concept also applies to loans, where understanding the interest rate and compounding period can help you minimize the total cost of borrowing.
After 5 years, the total amount in the account is $7213.02, and the interest earned is $213.02. This demonstrates the power of compound interest over time. By subtracting the principal from the final amount, we found the interest earned.
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