Spencer deposited $10 in an account earning 5% interest compounded annually. To the nearest cent, how much will he have in 3 years?
Understand the Problem
The question is asking how much money Spencer will have after 3 years if he deposits $10 in an account that earns 5% interest compounded annually. We'll use the formula for compound interest to calculate this.
Answer
Spencer will have $11.58 after 3 years.
Answer for screen readers
Spencer will have approximately $11.58 after 3 years.
Steps to Solve
- Identify the Compound Interest Formula
The formula for compound interest is given by:
$$ A = P(1 + r)^t $$
Where:
- ( A ) is the amount of money accumulated after n years, including interest.
- ( P ) is the principal amount (the initial amount of money).
- ( r ) is the annual interest rate (in decimal).
- ( t ) is the time the money is invested or borrowed for, in years.
- Substitute the Given Values
Now, we plug in the values:
- ( P = 10 )
- ( r = 0.05 ) (which is 5% expressed as a decimal)
- ( t = 3 )
So we substitute those into the formula:
$$ A = 10(1 + 0.05)^3 $$
- Calculate the Value Inside the Parentheses
Calculate ( 1 + r ):
$$ 1 + 0.05 = 1.05 $$
- Raise to the Power of t
Now calculate:
$$ (1.05)^3 $$
This equals about ( 1.157625 ).
- Multiply by the Principal
Multiply this result by the principal:
$$ A = 10 \times 1.157625 \approx 11.57625 $$
- Round to the Nearest Cent
Finally, we round ( 11.57625 ) to the nearest cent.
The result is ( 11.58 ).
Spencer will have approximately $11.58 after 3 years.
More Information
This calculation demonstrates how compound interest can effectively grow your investment over time. Even a small initial deposit, like $10, can accumulate significant interest over a few years!
Tips
- Forgetting to convert the percentage to a decimal (5% should be 0.05).
- Neglecting to round off to the nearest cent after calculations.
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