Question

the winner of a lottery chooses to receive annual payments of $190,000 at the end of each year for 25 years. if the current interest rate is 4.4%, find the present value (in dollars) of the payments. (round your answer to the nearest cent. see example 5 in this section.)

Explanation:

Step1: Identify given values

Annual payment $P = 190000$, time $n = 25$ years, interest rate $r = 0.044$

Step2: Use present value annuity formula

The formula for present value of an ordinary annuity is $PV = P \times \frac{1-(1+r)^{-n}}{r}$

Step3: Substitute values into formula

$$PV = 190000 \times \frac{1-(1+0.044)^{-25}}{0.044}$$

Step4: Calculate $(1.044)^{-25}$

$(1.044)^{-25} \approx 0.33277$

Step5: Compute numerator

$1 - 0.33277 = 0.66723$

Step6: Divide by interest rate

$\frac{0.66723}{0.044} \approx 15.1643$

Step7: Multiply by annual payment

$190000 \times 15.1643 \approx 2881217.05$

Answer:

2881217.05