Imagine that you are the lucky winner of a cash calendar lottery. This prize is a regular payment of $500 at the end of each month for the next two years. Suppose the best interest rate you could find was an account that pays 1.7% per annum, compounded monthly.

(a)What is the present value of this lottery prize? Give your answer rounded to the nearest cent.

(b) How many payments would need to be made for the prize to have a present value of $15,000? Give your answer rounded up to the nearest whole month.