You just won a prize of $$15,000$ at the local Invention Ideas show. You can receive the money all up front $($t$=0)$; OR$,$ you may choose to get $36$ monthly payments, with the first payment starting $7$ months from now. In both cases, your discount rate is $3\%$ APR. $($Assume all compounding is annual.$)$ Using an annuity formula, calculate the monthly payment that makes you indifferent between receiving the $$15,000$ today or in $36$ monthly installments starting in Month $7.$ The total value $($PV of the annuity$)$ received via the delayed starting payment stream $($derived by a formula, not a typed number$)$ should appear in Box $1.$ A variation of the constant annuity formula $($not a typed number$)$ should appear in Box $2$ on the spreadsheet to give the monthly payment amount. You must check this result by completing the table and summing all the present values of this monthly amount in Sum Column $1$; the total of the values in this Column should equal $$15,000.$

Across town, your friend has entered a similar contest, but the $41-$month prize money payout schedule is already set: $$400$ today $($immediately$),$ followed by $40$ monthly payments that grow this original payout at $2\mathrm{.}0\%$ APR. Your friend$$s discount rate is $6\%$ APR. $($Assume all compounding is annual$).$ What NPV does your friend receive from the prize? To do this, you must add the first $$400\mathrm{.}00$ payment to the PV of all $40$ of the future payments, determined by using a growing annuity formula. This formula $($not a typed number$)$ should appear in Box $3$ on the spreadsheet. You must check this result by completing the table and sum