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.)
To find the amount of an annuity, we can use the formula:
A = P(1 + r/n)^(n*t)
Where:
A is the final amount
P is the monthly payment
r is the interest rate (in decimal form)
n is the number of times the interest is compounded per year
t is the number of years
In this case, the monthly payment is $210, the interest rate is 8% (or 0.08 as a decimal), the interest is compounded continuously (n approaches infinity), and the period is 20 years.
First, we need to convert the interest rate to its equivalent per compounding period. Since the interest is compounded continuously, we do not need to adjust it.
Next, we plug the values into the formula:
A = 210(1 + 0.08/1)^(1*20)
Simplifying further:
A = 210(1.08)^20
Calculating (1.08)^20:
A ≈ 210 * 4.66096
A ≈ $978.40
Therefore, the amount in the annuity after 20 years would be approximately $978.40.