If $2,000 is invested at 5% compounded quarterly, what is the amount after 8 years? The amount after 8 years will be $◻. (Round to the nearest cent.)

Identify Values: Identify the principal amount (P), the annual interest rate (r), the number of times the interest is compounded per year (n), and the number of years the money is invested (t). P = $2,000 r = 5% or 0.05 n = 4 (since interest is compounded quarterly) t = 8 yearsCompound Interest Formula: Use the compound interest formula to calculate the final amount (A). The compound interest formula is A = P(1 + r/n)^(nt). Substitute the values into the formula: A = 2000(1 + 0.05/4)^(4*8)Calculate Values: Calculate the values inside the parentheses and the exponent. 1 + 0.05/4 = 1 + 0.0125 = 1.0125 4 * 8 = 32 Now the formula looks like this: A = 2000(1.0125)^(32)Calculate Amount: Calculate the amount after 8 years. A = 2000(1.0125)^(32) Use a calculator to find (1.0125)^(32): (1.0125)^(32) ≈ 1.489856 Now multiply this by the principal amount: A ≈ 2000 * 1.489856 A ≈ 2979.712Round Final Amount: Round the final amount to the nearest cent. A ≈ $2979.71

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If
$2,000 is invested at
5% compounded quarterly, what is the amount after 8 years?
The amount after 8 years will be
$◻.
(Round to the nearest cent.)

If $\$ 2,000$ is invested at $5 \%$ compounded quarterly, what is the amount after $8$ years? $\newline$ The amount after $8$ years will be $\$ \square$ . $\newline$ (Round to the nearest cent.)

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Algebra 1

Exponential growth and decay: word problems

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Q. If

\$ 2,000

is invested at

5 \%

compounded quarterly, what is the amount after

8

years?

\newline

The amount after

8

years will be

\$ \square

\newline

(Round to the nearest cent.)

Identify Values: Identify the principal amount $P$ , the annual interest rate $r$ , the number of times the interest is compounded per year $n$ , and the number of years the money is invested $t$ . $P = \$2,000$ $r = 5\%$ or $0.05$ $n = 4$ (since interest is compounded quarterly) $t = 8$ years
Compound Interest Formula: Use the compound interest formula to calculate the final amount $A$ . The compound interest formula is $A = P(1 + r/n)^{(nt)}$ . Substitute the values into the formula: $A = 2000(1 + 0.05/4)^{(4*8)}$
Calculate Values: Calculate the values inside the parentheses and the exponent. $\newline$ $1 + \frac{0.05}{4} = 1 + 0.0125 = 1.0125$ $\newline$ $4 \times 8 = 32$ $\newline$ Now the formula looks like this: $\newline$ $A = 2000(1.0125)^{32}$
Calculate Amount: Calculate the amount after $8$ years. $\newline$ $A = 2000(1.0125)^{32}$ $\newline$ Use a calculator to find $(1.0125)^{32}$ : $\newline$ $(1.0125)^{32} \approx 1.489856$ $\newline$ Now multiply this by the principal amount: $\newline$ $A \approx 2000 \times 1.489856$ $\newline$ $A \approx 2979.712$
Round Final Amount: Round the final amount to the nearest cent. $\newline$ $A \approx \$2979.71$