Amy Powell invested $8500 twice a year in an ordinary annuity at New York Securities for a period of 5 years at an annual interest rate of 10% compounded semiannually. Using the ordinary annuity table , calculate the total value of the annuity at the end of the 5-year period
To calculate the total value of the annuity at the end of the 5-year period, we need to use the ordinary annuity table and apply the compound interest formula.
First, let's break down the information given:
- Principal amount (P): Amy invested $8500 twice a year.
- Interest rate (r): The annual interest rate is 10%, compounded semiannually. So the semi-annual interest rate is 10% / 2 = 5%.
- Time period (t): Amy invested for 5 years. Since she invested twice a year, the number of periods would be 5 years x 2 = 10 semi-annual periods.
Now, let's use the ordinary annuity table to find the future value factor for the given interest rate and time period. The future value factor represents the amount by which the principal will be multiplied to give the total value at the end.
In this case, we need to find the future value factor for a semi-annual interest rate of 5% and 10 semi-annual periods (n). Referring to the ordinary annuity table, the future value factor for 5% interest rate and 10 periods is 1.62889.
Next, we need to multiply the future value factor by the principal amount to calculate the total value of the annuity at the end:
Total Value = Principal x Future Value Factor
Total Value = $8500 x 1.62889
Total Value = $13,847.65 (rounded to 2 decimal places)
Therefore, the total value of the annuity at the end of the 5-year period is approximately $13,847.65.