Sandra deposits $3000 in an ordinary annuity at the end of each semiannual period at 8% interest compounded semiannually. Find the amount she will have on deposit after 17 years
To find the amount Sandra will have on deposit after 17 years, we can use the formula for the future value of an ordinary annuity.
The future value (FV) of an ordinary annuity can be calculated using the following formula:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value
P = Payment amount
r = Interest rate per period
n = Number of periods
In this case, Sandra deposits $3000 at the end of each semiannual period, which means her payment amount (P) is $3000. The interest rate (r) is 8% divided by 2 (since it's compounded semiannually), which is 0.08 / 2 = 0.04. The number of periods (n) is 17 years multiplied by 2 (since it's compounded semiannually), which is 17 * 2 = 34.
Therefore, we can substitute these values into the formula:
FV = $3000 * [(1 + 0.04)^34 - 1] / 0.04
Now, we can calculate:
FV = $3000 * [1.783118732 - 1] / 0.04
FV = $3000 * 0.783118732 / 0.04
FV ≈ $58,967.92
Therefore, Sandra will have approximately $58,967.92 on deposit after 17 years.