Sofia has $7,306 in an account. The interest rate is 8% compounded annually. To the nearest cent, how much will she have in 2 years?
Understand the Problem
The question is asking to calculate the future value of an investment with compound interest. We need to use the compound interest formula to find out how much money Sofia will have in her account after 2 years, given an initial principal of $7,306 and an annual interest rate of 8%. Finally, we need to round the answer to the nearest cent.
Answer
$8521.27$
Answer for screen readers
$8521.27$
Steps to Solve
- Identify the compound interest formula
The formula for compound interest is: $A = P(1 + r)^t$ Where: $A$ = the future value of the investment/loan, including interest $P$ = the principal investment amount (the initial deposit or loan amount) $r$ = the annual interest rate (as a decimal) $t$ = the number of years the money is invested or borrowed for
- Plug in the values
We are given: $P = 7306$ $r = 8% = 0.08$ $t = 2$
Substituting these values into the formula, we get: $A = 7306(1 + 0.08)^2$
- Calculate the future value
Simplify the expression inside the parentheses: $A = 7306(1.08)^2$
Calculate $(1.08)^2$: $A = 7306 \times 1.1664$
Multiply: $A = 8521.2744$
- Round to the nearest cent
Rounding $8521.2744$ to the nearest cent (two decimal places) gives us $8521.27$
$8521.27$
More Information
Compound interest is a powerful tool for growing wealth over time, as the interest earned also earns interest in subsequent periods. In this case, Sofia's initial investment of $7,306 grew to $8,521.27 in just two years due to the effect of annual compounding.
Tips
A common mistake is forgetting to convert the percentage into a decimal before using it in the formula. Another common mistake is not rounding the final answer to the nearest cent as the question asks. Also, some people might use simple interest formula instead of the compound interest formula.
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