You have just won the lottery and you will receive 10 annual beginning-of-year payments of $5 million each. If you expect to earn a 9% compounded semi-annually, what will be the current value of the lottery payments?

Current value of lottery=$ 33,983,233.98

Explanation:

The value of the lottery is the Present of the annual cash flow discovered at the discount rate of 9% compounded semi annually.

Semi-annual rate = 9%/2 = 4.5%

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

A - 5,000,000/2 = 2,500,000. r - 4.5%, n - 2 * 10 = 20

The first payment is already in its present value term, hence it is already discounted.

The balance of 19 payments would be discounted as follows

PV = 2,500,000 * (1 - (1.045) ^ (-19) / 0.045

= 31,483,233.98

Current value of lottery = 2,500,000 + 31,483,233.98

=$ 33,983,233.98