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5000 dollars is placed in an account with an annual interest rate of
8.75%. How much will be in the account after 18 years, to the nearest cent?
Answer:

$5000$ dollars is placed in an account with an annual interest rate of $8.75 \%$ . How much will be in the account after $18$ years, to the nearest cent? $\newline$ Answer:

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Exponential growth and decay: word problems

Full solution

Q.

5000

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

8.75 \%

. How much will be in the account after

18

years, to the nearest cent?

\newline

Answer:

Identify Principal, Rate, Time: Identify the initial principal amount, the annual interest rate, and the time period. $\newline$ The initial principal amount $P$ is $\$5000$ . $\newline$ The annual interest rate $r$ is $8.75\%$ or $0.0875$ in decimal form. $\newline$ The time period $t$ is $18$ years.
Determine Interest Type: Determine the type of interest being applied. $\newline$ Since the problem does not specify compound interest or simple interest, we will assume compound interest is applied annually.
Use Compound Interest Formula: Use the compound interest formula to calculate the final amount in the account. $\newline$ The compound interest formula is $A = P(1 + r/n)^{(nt)}$ , where: $\newline$ $A$ 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. $\newline$ Since interest is compounded annually, $n = 1$ .
Substitute Values and Calculate: Substitute the values into the compound interest formula and calculate the final amount. $\newline$ $A = 5000(1 + 0.0875/1)^{(1*18)}$ $\newline$ $A = 5000(1 + 0.0875)^{18}$ $\newline$ $A = 5000(1.0875)^{18}$
Calculate Final Amount: Calculate the final amount using the values substituted into the formula. $\newline$ $A = 5000 \times (1.0875)^{18}$ $\newline$ $A = 5000 \times 4.33219$ (rounded to five decimal places) $\newline$ $A = 21660.95$
Round to Nearest Cent: Round the final amount to the nearest cent. $\newline$ The final amount in the account after $18$ years, rounded to the nearest cent, is $\$21660.95$ .

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