Determine the future value of an annuity due of $10,000 every year for 15 years given the interest rate is 5%.Group of answer choices$215,790$226,579.50$21,579None of the options.Next
Question
Determine the future value of an annuity due of 215,79021,579None of the options.Next
Solution
To calculate the future value of an annuity due, we use the formula:
FV = P * [(1 + r)^n - 1] / r * (1+r)
where: P = payment amount per period = $10,000 r = interest rate per period = 5% = 0.05 n = number of periods = 15 years
Step 1: Calculate (1 + r)^n (1 + 0.05)^15 = 2.07892818
Step 2: Subtract 1 from the result of step 1 2.07892818 - 1 = 1.07892818
Step 3: Divide the result of step 2 by r 1.07892818 / 0.05 = 21.5785636
Step 4: Multiply the result of step 3 by P 21.5785636 * 215,785.636
Step 5: Multiply the result of step 4 by (1+r) because it's an annuity due 226,574.918
So, the future value of the annuity due is approximately 226,579.50.
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