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.