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4800 dollars is placed in an account with an annual interest rate of
6.5%. How much will be in the account after 14 years, to the nearest cent?
Answer:

$4800$ dollars is placed in an account with an annual interest rate of $6.5 \%$ . How much will be in the account after $14$ years, to the nearest cent? $\newline$ Answer:

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Exponential growth and decay: word problems

Full solution

Q.

4800

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

6.5 \%

. How much will be in the account after

14

years, to the nearest cent?

\newline

Answer:

Determine interest calculation type: Determine the type of interest calculation. $\newline$ Since the interest is compounded annually, we will use the formula for compound interest: $A = P(1 + r/n)^{(nt)}$ . $\newline$ Here, $A$ is the amount of money accumulated after $n$ years, including interest. $\newline$ $P$ is the principal amount (the initial amount of money). $\newline$ $r$ is the annual interest rate (decimal). $\newline$ $n$ is the number of times that interest is compounded per year. $\newline$ $t$ is the time the money is invested for in years.
Identify values: Identify the values of $P$ , $r$ , $n$ , and $t$ .
$P = 4800$ dollars (the initial deposit).
$r = 6.5\%$ or $0.065$ (the annual interest rate in decimal form).
$n = 1$ (since the interest is compounded annually).
$t = 14$ years (the time period the money is invested).
Substitute values into formula: Substitute the values into the compound interest formula. $\newline$ $A = 4800(1 + 0.065/1)^{(1*14)}$ $\newline$ Simplify the equation. $\newline$ $A = 4800(1 + 0.065)^{14}$ $\newline$ $A = 4800(1.065)^{14}$
Calculate amount after $14$ years: Calculate the amount after $14$ years. $\newline$ $A = 4800 \times (1.065)^{14}$ $\newline$ Use a calculator to find $(1.065)^{14}$ . $\newline$ $(1.065)^{14} \approx 1.697848$ $\newline$ Now multiply this by the principal amount. $\newline$ $A \approx 4800 \times 1.697848$ $\newline$ $A \approx 8145.67$

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