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What sum of money will grow to \( \$ 2700.38 \) in five years at \( 2.5 \% \) compounded quarterly? The sum of money is \( \$ \) (Round to the nearest cent as needed. Round all intermediate values to

User Kemal
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1 Answer

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To find the initial sum of money that will grow to $2700.38 in five years with a 2.5% interest rate compounded quarterly, we can use the formula for compound interest:

Future Value = Principal * (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods * Number of Years)

In this case, the future value is $2700.38, the interest rate is 2.5%, the compounding is quarterly (4 times a year), and the number of years is 5.

$2700.38 = Principal * (1 + (0.025 / 4))^(4 * 5)

Now let's solve for the principal:

Principal = $2700.38 / (1 + (0.025 / 4))^(4 * 5)

Principal = $2700.38 / (1 + 0.00625)^(20)

Principal = $2700.38 / (1.00625)^(20)

Principal = $2700.38 / 1.131825

Principal = $2389.39 (rounded to the nearest cent)

Therefore, the initial sum of money needed to grow to $2700.38 in five years at a 2.5% interest rate compounded quarterly is approximately $2389.39.

User Sagar Chorage
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