Question

A lottery claims its grand prize is 10 million payable over 20 years at 500000 per year. if the first payment is made immediately what is this grand prize really worth use interest rate of 6%?

Answer 1

6079058.246

Explanation:

This is annuity due problem, where the payment is made at the beginning of the year. Here, also the payment is made immediately.

Now, applying Annuity due formula

PV= A(1-(1+i)^-n)/i *(1+i)

So, PV is present value of Grand. That is what we want to find

A= annuity (the yearly payment) in this case, it is 500,000

i= is interest rate which is 6%

n= number of years, 20 years

putting all these values in the formula

PV=500,000(1-(1+0.06)^-20)/0.06 *(1+0.06)

we get 6,079,058.246

This is what the grand price of 10 M worth today.