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Savannah invested
$1500 in an account that pays
3% interest compounded annually. Assuming no deposits or withdrawals are made, find how much money Savannah would have in the account 20 years after her initial investment. Round your answer to the nearest whole number.
Answer: $ □

Savannah invested $\$ 1500$ in an account that pays $3 \%$ interest compounded annually. Assuming no deposits or withdrawals are made, find how much money Savannah would have in the account $20$ years after her initial investment. Round your answer to the nearest whole number. $\newline$ Answer: $ \(\square\)

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Exponential growth and decay: word problems

Full solution

Q. Savannah invested

\$ 1500

in an account that pays

3 \%

interest compounded annually. Assuming no deposits or withdrawals are made, find how much money Savannah would have in the account

20

years after her initial investment. Round your answer to the nearest whole number.

\newline

Answer: $ \(\square\)

Identify Variables: 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 $t$ . $P = \$1500$ , $r = 3\%$ or $0.03$ , $n = 1$ (since it's compounded annually), $t = 20$ years.
Compound Interest Formula: Use the compound interest formula $A = P(1 + r/n)^{(nt)}$ to find the amount of money $A$ that Savannah will have in the account after $t$ years. $\newline$ Substitute the known values into the formula: $A = 1500(1 + 0.03/1)^{(1*20)}$ .
Simplify and Calculate Exponent: Simplify the expression inside the parentheses and then calculate the exponent. $\newline$ $A = 1500(1 + 0.03)^{20} = 1500(1.03)^{20}$ .
Calculate Value: Calculate the value of $(1.03)^{20}$ using a calculator. $\newline$ $(1.03)^{20} \approx 1.80611$ .
Multiply Principal Amount: Multiply the principal amount by the result from Step $4$ to find the total amount in the account after $20$ years. $\newline$ $A = 1500 \times 1.80611 \approx 2709.165$ .
Round to Nearest Dollar: Round the result to the nearest whole number as the problem asks for the answer in whole dollars. $\newline$ $A \approx \$2710$ .

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