Questions: Scott Jackson invested 1000 four times a year in an annuity due at All-Star Investments for a period of 3 years at an interest rate of 12% compounded quarterly. Using the ordinary annuity table, calculate the total value of the annuity due at the end of the 3-year period.

Solution Steps

The annual interest rate is given as \( 12\% \). To find the quarterly interest rate, we divide by \( 4 \): \[ \text{Quarterly Interest Rate} = \frac{12\%}{4} = 3\% = 0.03 \]

Scott Jackson invests for \( 3 \) years, with \( 4 \) investments per year. Therefore, the total number of periods is: \[ \text{Total Periods} = 3 \times 4 = 12 \]

Using the ordinary annuity table for \( 12\% \) interest over \( 12 \) periods, we find: \[ \text{Ordinary Annuity Value} = 17.5487 \]

Since this is an annuity due, we adjust the ordinary annuity value by multiplying it by \( (1 + \text{Quarterly Interest Rate}) \): \[ \text{Annuity Due Value} = 17.5487 \times (1 + 0.03) = 17.5487 \times 1.03 = 18.075161 \]

Finally, we multiply the adjusted annuity due value by the periodic payment of \( 1000 \): \[ \text{Total Value} = 1000 \times 18.075161 = 18075.161 \]

Final Answer