If an annuity was set up for semiannual payments at the beginning of each period in the amount of $1,478, what would be the value of this annuity after 9 ½ years with interest compounded daily at a rate of 3.75%
To calculate the value of an annuity, we need to use the formula for the future value of a set of cash flows. The formula is as follows:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value of the annuity
P = Payment amount per period
r = Interest rate per period
n = Number of periods
In this case, the payment amount per period is $1,478, the interest rate per period is 3.75% compounded daily, and the number of periods is 9 ½ years or 19 half-years (since it's semiannual payments).
Step 1: Convert the annual interest rate to a daily rate.
The annuity interest rate is 3.75% annually, which we need to convert to a daily rate. To do this, we divide the annual rate by the number of days in a year (365 days):
Daily interest rate = (1 + Annual interest rate)^(1/number of days in a year) - 1
= (1 + 0.0375)^(1/365) - 1
Step 2: Calculate the future value of the annuity using the formula:
FV = P * [(1 + r)^n - 1] / r
= $1,478 * [(1 + Daily interest rate)^19 - 1] / Daily interest rate
Using a calculator or spreadsheet, you can substitute the values into the formula to find the future value of the annuity after 9 ½ years with interest compounded daily at a rate of 3.75%.