Question

A major lottery advertises that it pays the winner $10 million. however this prize money is paid at the rate of $500,000 each year (with the first payment being immediate) for a total of 20 payments. what is the present value of this prize at 10% interest compounded annually

Answer 1

The present value formula is :

P(1 + i)⁻ⁿ

i = Compound interest.

P = installment

n = the periods

In our case :

n = 20

i = 10%

P = 10000000

Doing the substitution we have :

10000000 × (1.1)⁻²⁰

(1.1)⁻²⁰ = 0.1486

Doing the multiplication.

10000000 × 0.1486 = 1486000

PV = 1486000

Answer 2

Given, a major lottery advertises that it pays the winner $10 million.

The prize money is paid at the rate of $500,000 each year for a total of 20 payments. P = 500000 ∑ (1 + 0.10) ^ (-i)  = 4682460.

The Present value of the prize with 10% interest is Rs. 4682460.