Find the amount of an annuity if $210/month is paid into it for a period of 20 yr, earning interest at the rate of 8%/year compounded continuously. (Round your answer to two decimal places.)
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To find the amount of an annuity, we can use the formula for the future value of an annuity:
A = P * (e^(rt) - 1) / r
Where:
A = amount of the annuity
P = monthly payment
r = interest rate per compounding period
t = number of compounding periods
In this case, the monthly payment is $210, the interest rate is 8%/year, and the period is 20 years. We need to convert the interest rate to a decimal and the period to the number of compounding periods.
First, let's convert the interest rate to a decimal. Divide the interest rate by 100:
8% / 100 = 0.08
Now, let's calculate the number of compounding periods. Since the annuity is paid monthly, the number of compounding periods will be the number of months in 20 years:
20 years * 12 months/year = 240 months
Now we have all the information needed to calculate the amount of the annuity:
A = $210 * (e^(0.08 * 240) - 1) / 0.08
Using a calculator, we can calculate the value of e^(0.08 * 240) to be approximately 126.5165404.
A = $210 * (126.5165404 - 1) / 0.08
A = $210 * (125.5165404) / 0.08
A ≈ $329,137.86
Therefore, the amount of the annuity is approximately $329,137.86.