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A savings account earns an interest rate of
2.75% compounded monthly for an account with an initial deposit of
$5,000. How much money will be in the account after 8 years? Round your answer to the nearest hundredth.

A savings account earns an interest rate of $2.75 \%$ compounded monthly for an account with an initial deposit of $\$ 5,000$ . How much money will be in the account after $8$ years? Round your answer to the nearest hundredth.

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Exponential growth and decay: word problems

Full solution

Q. A savings account earns an interest rate of

2.75 \%

compounded monthly for an account with an initial deposit of

\$ 5,000

. How much money will be in the account after

8

years? Round your answer to the nearest hundredth.

Calculate Compound Interest: Calculate the compound interest using the formula. $A = 5000(1 + 0.0275/12)^{(12\times8)}$
Simplify Expression: Simplify the expression inside the parentheses. $\newline$ $A = 5000(1 + 0.00229166667)^{96}$
Add Numbers: Add the numbers inside the parentheses. $\newline$ $A = 5000(1.00229166667)^{96}$
Calculate Exponent: Calculate the exponent part. $\newline$ $A = 5000 \times (1.00229166667)^{96}$
Use Calculator: Use a calculator to raise $1.00229166667$ to the $96^{th}$ power. $\newline$ $A \approx 5000 \times 1.246853823$
Multiply Result: Multiply the result by the initial deposit. $\newline$ $A \approx 5000 \times 1.246853823$ $\newline$ $A \approx 6234.269115$
Round Answer: Round the answer to the nearest hundredth. $\newline$ $A \approx \$6234.27$

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