To solve this problem, we need to use the formula for compound interest, which is given by:
A = P(1 + r/n)^(nt)
Here,
P represents the principal amount (the initial amount of money), which is $9500.
r is the annual interest rate represented as a decimal, which is 6.2/100, or 0.062.
n represents the number of compounding periods per year, which is 4 as the interest is compounded quarterly.
t is the time the money is invested in years, which is 6 in this case.
Step #1: Calculate the Number of Compounding Periods
The total number of compounding periods is calculated by multiplying the number of compounding periods per year by the number of years the money is invested for.
So, total_periods = n*t = 4 * 6 = 24 compounding periods.
Step #2: Calculate the Final Amount Using the Compound Interest Formula
The compound interest formula calculates the final amount by compounding the interest over the specified number of periods.
Amount = P * (1 + r/n)^(nt) = 9500 * (1 + 0.062/4)^(24)
The result of this calculation is the amount of money that would be in the account after 6 years, before it is rounded.
Step #3: Rounding the Final Amount
The final amount calculated in Step #2 is then rounded to the nearest cent, i.e., to two decimal places. This can be achieved by using standard rounding rules - if the value at the third decimal place is 5 or more, we would round up, otherwise, we would leave the second decimal place as is.
Amount_rounded = Rounded final amount = 13741.74 (rounded to the nearest cent)
So, at the end of 6 years, the amount in the account would be $13,741.74 when compounded quarterly.