Respuesta :
Answer:
The present value of Frank Ormsby's lottery winnings: $638,517
Explanation:
Please find the below for detailed calculations and explanations:
The present value of Frank Ormsby's winnings is the net present value of the annuity, in which equal annual payment of $75,000 will be paid in the next 20 years and the discount rate is the rate of return at 10%.
Thus, we apply the present value formula for determining present value of the annuity to calculate the present value of his winnings as followed:
PV = (C/i) x [ 1 - (1+i)^(-n)] = (75,000/0.1) x [1 - 1.1^(-20)] = $638,517
The present value of Mr. Ormsby Winnings will be $ 638,550 if the investment can be made at a 10% rate of return.
What is the Present Value of Annuity?
The present value of the annuity is the present value of future payments from pensions, taking into account the stated amount of the rebate, or the discounted amount. If the discount rate is high, the current annuity amount decreases.
[tex]\rm\,PV = P\times\,\dfrac{1 - (1+r)^{-n}}{r}\\[/tex]
As per the given information,
Value of each installment (P) is equal to $75,000
Rate (r) = 10%
Number of periods(n) is equal to 20
[tex]\rm\,PV = P\times\,\dfrac{1 - (1+r)^{-n}}{r}\\\\\\\rm\,PV = 75,000\times\,\dfrac{1 - (1+0.10)^{-20}}{0.10}\\\\\\\rm\,PV = 75,000\times\,\dfrac{(1 - 0.1483)}{0.10}\\\\\\rm\,PV = 75,000\times\,\dfrac{0.8514}{0.10}\\\\\rm\,PV = 75,000\times\, 8.514\\\\\rm\,PV = \$\, 638,550[/tex]
Hence, if Mr. Ormsby can invest money at 10% rate of return, the present value of the winnings will be $638,550
To learn more about Present Value of Annuity, refer to the link:
https://brainly.com/question/25792915
