QuestionMay 22, 2025

Becky deposits 12,000 into an account with an interest rate of 7% that is compounded monthly.Rounding to the nearest dollar, what is the balance after 7 years? 19,560 17,545 18,720 13,402

Becky deposits 12,000 into an account with an interest rate of 7% that is compounded monthly.Rounding to the nearest dollar, what is the balance after 7 years? 19,560 17,545 18,720 13,402
Becky deposits 12,000 into an account with an interest rate of 7%  that is
compounded monthly.Rounding to the nearest dollar, what is the balance
after 7 years?
 19,560
 17,545
 18,720
 13,402

Solution
4.2(420 votes)

Answer

\19,269 Explanation 1. Identify the formula for compound interest Use the formula for compound interest: **A = P \left(1 + \frac{r}{n}\right)^{nt}**, where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years. 2. Substitute the given values into the formula P = 12000, r = 0.07, n = 12, t = 7. Substitute these into the formula: A = 12000 \left(1 + \frac{0.07}{12}\right)^{12 \times 7}. 3. Calculate the compound interest Compute A = 12000 \left(1 + \frac{0.07}{12}\right)^{84}. First, calculate \frac{0.07}{12} \approx 0.0058333. Then, 1 + 0.0058333 \approx 1.0058333. Raise this to the power of 84: 1.0058333^{84} \approx 1.605781. Finally, multiply by 12000: A \approx 12000 \times 1.605781 \approx 19269.37. 4. Round to the nearest dollar Round 19269.37 to the nearest dollar, which gives 19269.

Explanation

1. Identify the formula for compound interest<br /> Use the formula for compound interest: **$A = P \left(1 + \frac{r}{n}\right)^{nt}$**, where $A$ is the amount, $P$ is the principal, $r$ is the annual interest rate, $n$ is the number of times interest is compounded per year, and $t$ is the time in years.<br /><br />2. Substitute the given values into the formula<br /> $P = 12000$, $r = 0.07$, $n = 12$, $t = 7$. Substitute these into the formula: $A = 12000 \left(1 + \frac{0.07}{12}\right)^{12 \times 7}$.<br /><br />3. Calculate the compound interest<br /> Compute $A = 12000 \left(1 + \frac{0.07}{12}\right)^{84}$. First, calculate $\frac{0.07}{12} \approx 0.0058333$. Then, $1 + 0.0058333 \approx 1.0058333$. Raise this to the power of 84: $1.0058333^{84} \approx 1.605781$. Finally, multiply by 12000: $A \approx 12000 \times 1.605781 \approx 19269.37$.<br /><br />4. Round to the nearest dollar<br /> Round $19269.37$ to the nearest dollar, which gives $19269$.
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