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 |
| :-------- | :------ | :--------- | :------ |
| $7500 | 4.5 % | monthly | 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 $9388.47
(Round to the nearest hundredth as needed.)
b. Find the interest earned.
The amount of interest earned is $ $\square$
(Round to the nearest hundredth as needed.)
Answer (1)
Calculate the interest earned by subtracting the principal amount from the amount after 5 years.
Interest earned = Amount after 5 years - Principal amount
Interest earned = $9388.47 - $7500
The amount of interest earned is $\boxed{ 1888.47} .
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. 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.
Calculating the Interest The principal amount is $7500, and the amount after 5 years is 9388.47. T h ere f ore , t h e in t eres t e a r n e d i s : I n t eres t = A m o u n t − P r in c i p a l $Interest = $9388.47 - 7500 $Interest = 1888.47 $
Final Answer The amount of interest earned is $1888.47.
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're comparing two savings accounts: one offers simple interest, and the other offers compound interest. By calculating the future value of your investment under both scenarios, you can see which account will yield a higher return over time. This knowledge empowers you to make strategic choices that maximize your financial growth.
