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Edgar has $30$ $\$$ in an account that earns $5\%$ interest compounded annually. To the nearest cent, how much interest will he earn in $2$ years? $\$$ ____

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Exponential growth and decay: word problems

Full solution

Q. Edgar has

30

\$

in an account that earns

5\%

interest compounded annually. To the nearest cent, how much interest will he earn in

2

years?

\$

____

Identify values: Identify the principal amount, interest rate, and time period. $\newline$ Edgar has $\$30$ in an account, which is the principal amount $P$ . $\newline$ The interest rate $r$ is $5\%$ , or $0.05$ when expressed as a decimal. $\newline$ The time period $t$ is $2$ years.
Use compound interest formula: Use the compound interest formula to calculate the future value (FV). $\newline$ The compound interest formula is $FV = P(1 + r/n)^{(nt)}$ , where: $\newline$ $P$ = principal amount ($\$\(30\))\(\newline\)\(r\) = annual interest rate (\(0.05\))\(\newline\)\(n\) = number of times the interest is compounded per year (\(1\), since it's compounded annually)\(\newline\)\(t\) = number of years the money is invested or borrowed for (\(2\))
Substitute values: Substitute the values into the compound interest formula.\(\newline\)\(FV = 30(1 + 0.05/1)^{(1*2)}\)\(\newline\)\(FV = 30(1 + 0.05)^{(2)}\)\(\newline\)\(FV = 30(1.05)^{(2)}\)
Calculate future value: Calculate the future value after \(2\) years.\(\newline\)\(FV = 30(1.05)^{2}\)\(\newline\)\(FV = 30(1.1025)\)\(\newline\)\(FV = 33.075\)
Calculate interest earned: Calculate the interest earned by subtracting the principal from the future value.\(\newline\)Interest = \(FV - P\)\(\newline\)Interest = \(33.075 - 30\)\(\newline\)Interest = \(3.075\)
Round interest: Round the interest to the nearest cent.\(\newline\)Interest \(\approx\) \(\$3.08\)

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