hermoine won $$360,000$ from the minnesota lottery. she can receive the money two ways. she can receive a monthly payment of $$1500$ for the next $20$ years. she can also receive a lump$-$sum payment which would be equivalent to the present value of the $$1500$ payments over the $20$ years using an interest rate of $4\mathrm{.}25\%$ compounded monthly. find the value of the lump$-$sum payment