Derek deposited $7,615 in an account earning 10% interest compounded annually. To the nearest cent, how much interest will he earn in 2 years?
Understand the Problem
The question asks how much interest Derek will earn in 2 years on a deposit of $7,615 at an annual interest rate of 10%, compounded annually. This involves using the compound interest formula.
Answer
The interest earned is $1594.15.
Answer for screen readers
The interest Derek will earn in 2 years is $1594.15.
Steps to Solve
- Identify the formula for compound interest
The formula for compound interest is given by:
$$ A = P(1 + r)^n $$
Where:
- $A$ = the amount of money accumulated after n years, including interest.
- $P$ = the principal amount (the initial deposit).
- $r$ = the annual interest rate (as a decimal).
- $n$ = the number of years the money is invested or borrowed.
- Substitute the known values into the formula
Given:
- Principal amount, $P = 7615$
- Annual interest rate, $r = 0.10$
- Number of years, $n = 2$
Thus, substituting these values into the formula gives:
$$ A = 7615(1 + 0.10)^2 $$
-
Calculate the accumulated amount, (A)
Now we compute:
$$ A = 7615(1.10)^2 $$
Calculating ( (1.10)^2 ):
$$ (1.10)^2 = 1.21 $$
So:
$$ A = 7615 \times 1.21 $$
Now, calculate ( A ):
$$ A = 9209.15 $$ -
Calculate the interest earned
The interest earned is found by subtracting the principal from the total amount:
$$ \text{Interest} = A - P $$
Substituting the values gives:
$$ \text{Interest} = 9209.15 - 7615 $$
Calculating gives:
$$ \text{Interest} = 1594.15 $$
The interest Derek will earn in 2 years is $1594.15.
More Information
Derek's investment growth reflects the power of compound interest, where interest is earned not only on the initial deposit but also on the accumulated interest from previous periods. This is a key principle in finance that allows savings to grow faster over time.
Tips
- Forgetting to convert the percentage to a decimal before using it in calculations.
- Miscalculating ( (1 + r)^n ) can lead to errors in the final amount and, consequently, the interest earned.
AI-generated content may contain errors. Please verify critical information
