Problem

Find the present value of an ordinary annuity which has payments of $\$ 1400$ per year for 14 years at $8 \%$ compounded annually.

Answer

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Answer

\(\boxed{11541.93}\)

Steps

Step 1 :Given an ordinary annuity with annual payments of $1400 for 14 years at an interest rate of 8% compounded annually, we are to find the present value of the annuity.

Step 2 :The present value of an ordinary annuity can be calculated using the formula: \(PV = PMT \times \frac{(1 - (1 + r)^{-n})}{r}\) where: \(PV\) is the present value, \(PMT\) is the annual payment, \(r\) is the interest rate per period, and \(n\) is the number of periods.

Step 3 :Substituting the given values into the formula, we have: \(PMT = 1400\), \(r = 0.08\), and \(n = 14\).

Step 4 :Calculating the present value, we get: \(PV = 1400 \times \frac{(1 - (1 + 0.08)^{-14})}{0.08} = 11541.93177614468\)

Step 5 :Rounding to two decimal places, the present value of the annuity is approximately $11541.93.

Step 6 :\(\boxed{11541.93}\)

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