Calculate the present value of an annuity due providing $200 every year for 4 years given the interest rate is 5%.Group of answer choicesNone of the options.$730.48$744.66$709.20
Question
Calculate the present value of an annuity due providing 730.48709.20
Solution
The present value of an annuity due can be calculated using the following formula:
PV = PMT * [(1 - (1 + r)^-n) / r] * (1 + r)
where:
- PV is the present value of the annuity due,
- PMT is the amount of each annuity payment,
- r is the interest rate per period, and
- n is the number of periods.
In this case, PMT = $200, r = 5% or 0.05, and n = 4 years.
Substituting these values into the formula gives:
PV = $200 * [(1 - (1 + 0.05)^-4) / 0.05] * (1 + 0.05)
Calculating the expression in the square brackets first:
= $200 * [(1 - (1.05)^-4) / 0.05] * 1.05
= $200 * [(1 - 0.822702474) / 0.05] * 1.05
= $200 * [0.177297526 / 0.05] * 1.05
= $200 * 3.54595052 * 1.05
= $744.66
So, the present value of the annuity due is $744.66.
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