Twice a year for 15 years, Warren Ford invested $1,700 compounded semiannually at 6% interest. What is the value of this annuity due? (p. 319)
80,878.21
To calculate the value of the annuity due, we can use the formula:
A = P * ((1 + r)^n - 1) / r
Where:
A = Value of annuity due
P = Periodic payment
r = Interest rate per compounding period
n = Number of compounding periods
In this case, Warren Ford invested $1,700 twice a year for 15 years, so:
P = $1,700
r = 6% (or 0.06)
n = 15 years * 2 compounding periods per year = 30 compounding periods
Substituting the values into the formula:
A = $1,700 * ((1 + 0.06)^30 - 1) / 0.06
Now we can calculate the value of the annuity due.
To find the value of this annuity due, we can use the formula for the future value of an annuity:
Future Value = P * [(1 + r)^n - 1] / r
Where:
P = Payment amount per period
r = Interest rate per period
n = Number of periods
In this case, the payment amount per period is $1,700, the interest rate per period is 6% (or 0.06), and the number of periods is 2 times a year for 15 years, which is a total of 2 * 15 = 30 periods.
Plugging in these values into the formula, we have:
Future Value = $1,700 * [(1 + 0.06)^30 - 1] / 0.06
Now, let's calculate this value:
Future Value = $1,700 * [(1.06)^30 - 1] / 0.06
To simplify the calculations, we can use a calculator or a spreadsheet program. Evaluating this expression, we find:
Future Value = $1,700 * [1.971261 - 1] / 0.06
Future Value = $1,700 * 0.971261 / 0.06
Future Value ≈ $1,700 * 16.18768
Future Value ≈ $27,527.95
Therefore, the value of this annuity due is approximately $27,527.95.