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7400 dollars is placed in an account with an annual interest rate of
8%. How much will be in the account after 19 years, to the nearest cent?
Answer:

$7400$ dollars is placed in an account with an annual interest rate of $8 \%$ . How much will be in the account after $19$ years, to the nearest cent? $\newline$ Answer:

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Exponential growth and decay: word problems

Full solution

Q.

7400

dollars is placed in an account with an annual interest rate of

8 \%

. How much will be in the account after

19

years, to the nearest cent?

\newline

Answer:

Identify Inputs: Identify the initial principal amount, the annual interest rate, and the time period. $\newline$ The initial principal amount $P$ is $\$7400$ , the annual interest rate $r$ is $8\%$ or $0.08$ in decimal form, and the time period $t$ is $19$ years.
Determine Interest Type: Determine the type of interest being applied. $\newline$ If the problem does not specify, we typically assume the interest is compounded annually.
Use Compound Interest Formula: Use the formula for compound interest to calculate the future value of the investment. $\newline$ The compound interest formula is $A = P(1 + \frac{r}{n})^{nt}$ , where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount, $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. $\newline$ Since the interest is compounded annually, $n = 1$ .
Substitute Values: Substitute the given values into the compound interest formula. $\newline$ $A = 7400(1 + \frac{0.08}{1})^{(1\times19)}$
Calculate Future Value: Calculate the future value of the investment. $\newline$ $A = 7400(1 + 0.08)^{19}$ $\newline$ $A = 7400(1.08)^{19}$
Perform Calculation: Perform the calculation. $\newline$ $A = 7400 \times (1.08)^{19}$ $\newline$ $A = 7400 \times 4.29229$ (rounded to five decimal places) $\newline$ $A = 31763.346$ (rounded to three decimal places)
Round Final Answer: Round the final answer to the nearest cent. $\newline$ $A \approx \$31,763.35$

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