You have decided to place $645 in equal deposits every month at the beginning of the month into a savings account earning 13.79 percent per year, compounded monthly for the next 12 years. The first deposit is made today. How much money will be in the account at the end of that time period?
Round the answer to two decimal places.
To calculate how much money will be in the savings account at the end of 12 years when you’re making equal monthly deposits at the beginning of each month, we can use the formula for future value in a compound interest scenario:
\[FV = PMT \times \frac{(1 + r)^n – 1}{r},\]
Where:
– \(FV\) is the future value of the savings account.
– \(PMT\) is the monthly deposit.
– \(r\) is the monthly interest rate.
– \(n\) is the number of compounding periods.
In this case:
– \(PMT = $645\) (the equal monthly deposit)
– \(r = \frac{13.79\%}{12} = 0.0115\) (the monthly interest rate, calculated from the annual rate)
– \(n = 12 \times 12 = 144\) (the number of compounding periods over 12 years)
Now, let’s plug these values into the formula and calculate the future value:
\[FV = $645 \times \frac{(1 + 0.0115)^{144} – 1}{0.0115}\]
Calculating the exponent and subtracting 1 inside the parentheses:
\[FV = $645 \times \frac{(1.0115)^{144} – 1}{0.0115}\]
Using a calculator to evaluate \((1.0115)^{144}\) and subtracting 1:
\[FV \approx $645 \times \frac{3.8696 – 1}{0.0115}\]
Now, subtract 1 from 3.8696:
\[FV \approx $645 \times \frac{2.8696}{0.0115}\]
Finally, divide to find the future value:
\[FV \approx $249,610.43\]
So, at the end of 12 years, with monthly deposits of $645 at the beginning of each month into a savings account earning an annual interest rate of 13.79 percent, compounded monthly, there will be approximately $249,610.43 in the account.
It’s important to note that this calculation assumes no withdrawals or additional deposits during the 12-year period and that the interest is compounded monthly. The actual amount in the account may vary if you make any changes to the deposit schedule or if the interest rate changes.
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