Question

A "Name That Tune" contest has a grand prize of $500,000. However, the contest stipulates that the winner will receive just $200,000 immediately, and $30,000 at the end of each of the next 10 years. Assuming that one can earn 8% on their money, how much has the contest winner actually won?
(A) 1,302
(B) $201,302
(C) $401,302
(D) $500,000
(E) None of the above

Answer 1

Answer:

The correct answer is (C) $401,302

Explanation:

To get how much the contest winner actually won, we have to calculate the amount receive at the end of each year discounted at this moment. Then,  we added  all the payments.  

For example, the first payment in  $200,000 at this moment,  so we add  $200,000.  

At the end of the first year we receive $30,000, and the rate of discount is 8%

The formula of discount is P=A/ (1+r)ⁿ

A=Final amount  

P= Principal

r= interest rate

n= time

Year 1 = A/ (1+r)ⁿ =$30,000/1,08¹= 27777,77

Year 2 =$30,000/1,08²= 25720,16

Year 3=23814,96

Year 4=22050,89

Year 5=20417,49

Year 6=18905,08

Year 7=17504,71

Year 8=16208,06

Year 9=15007,46

Year 10=13895,80

 

Total  401302,44