$100 is deposited at the beginning of every week for five years in an account that pays 14%/a, compounded weekly.
a. What type of annuity is this?
b. Find the future value of the annuity using the formula.
a. This is an example of a recurring deposit annuity, where a fixed amount is deposited at regular intervals over a specific period of time.
b. To calculate the future value of the annuity, we can use the formula:
FV = P * (1 + r/n)^(n*t) - 1) / (r/n)
Where:
FV is the future value of the annuity
P is the periodic payment or deposit amount
r is the annual interest rate in decimal form
n is the number of compounding periods per year
t is the number of years
In this case, the deposit amount is $100, the interest rate is 14% (or 0.14 in decimal form), and the compounding frequency is weekly, so n = 52. The total number of years is 5. Plugging these values into the formula, we get:
FV = 100 * (1 + 0.14/52)^(52*5) - 1) / (0.14/52)
After performing the calculations, the future value of the annuity is approximately $29,682.92.