Barbara Murphy invested $3000 four times a year in an annuity due at Southern Trust Company for a period of 4 years at an interest rate of 8% compounded quarterly. Using the ordinary annuity table, calculate the total value of the annuity due at the end of the 4-year period.$
Solution
To calculate the total value of the annuity due at the end of the 4-year period, we need to use the formula for the future value of an annuity due. The formula is:
FV = P * [(1 + r/n)^(nt) - 1] * (1+r/n) / (r/n)
Where: FV = future value of the annuity P = amount invested each period ($3000) r = annual interest rate (8% or 0.08) n = number of times the interest is compounded per year (4) t = number of years the money is invested for (4)
First, we need to calculate the value inside the brackets.
(1 + r/n)^(nt) - 1 = (1 + 0.08/4)^(4*4) - 1 = 1.377127764
Then, we multiply this by (1+r/n) to account for the annuity due being at the beginning of the period.
1.377127764 * (1+0.08/4) = 1.417282051
Finally, we divide this by (r/n) and multiply by the amount invested each period.
FV = 21259.23
So, the total value of the annuity due at the end of the 4-year period is approximately $21259.23.
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