Question

You won the lottery and may choose between Prize 1, which would pay you $50,000 today and $200,000 at the end of 10 years OR receive $50,000 today plus some annuity at the end of each year for 10 years. Using an interest rate of 5%, which of the following comes closest to the annuity that will make the present value of both prizes the same?

a. $172,782.65.
b. $38,431.68.
c. $122,782.65.
d. $15,900.91.

Answer 1

Annual payment= $15,900.91

Step-by-step explanation:

First, we need to calculate the present value of Prize 1:

PV= FV / (1 + i)^n

PV= 50,000 + [200,000 / (1.05^10)]

PV= $172,782.65

Now, we need to determine the annuity that would make equal both prizes:

Difference= 172,782.65 - 50,000= $122,782.65

To calculate the annuity that would have a PV of $122,782.65; we need to use the following formula:

Annual payment= (PV*i) / [1 - (1+i)^(-n)]

Annual payment= (122,782.65*0.05) / [1 - (1.05^-10)]

Annual payment= $15,900.91