Question

In: Accounting

You just won a contest! You will receive $50,000 a year for 30 years, starting today....

You just won a contest! You will receive $50,000 a year for 30 years, starting today. If you can earn 10 percent on your investments, what are your winnings worth today?

A. $150,000.00
B. $333,333.33
C. $436,510.50
D. $450,000.00
E. $518,480.30

Expert Solution

Correct answer is E.

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So you will receive $50000 every year at the starting of the year. pls note that the series of payment is an annuity due.

Present Value of an annuity due is used to determine the present value of a stream of equal payments where the payment occurs at the beginning of each period.

If,

Periodic payment (P) = 50000

Interest rate (i) = 0.1

Time period (n) = 30

Then PV of annuity due = P * (1 + i) [1 - {(1+ i)^-n}/i]

Lets put all the values in the formula to find PV of annuity due,

PV of annuity due = 50000* (1 + 0.1) [{1- (1 + 0.1)^- 30}/ 0.1]

= 50000* (1.1) [{1- (1.1)^- 30}/ 0.1]

= 55000[{1- 0.0573085533}/ 0.1]

= 55000[0.9426914467/ 0.1]

= 55000* 9.42691

= 518480.05

So PV of annuity due is $518480.05

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Hope this answer your query.

Feel free to comment if you need further assistance. J

ekkarill92 answered 8 months ago

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