Hello! I'm struggling on the following question and wanted to make sure I was doing it correctly! I found that the Net present value was -z + 217.39 *z as well as a z* value of $11,814.60, am I on the right track here?

1) Consumer A has access to a perfect capital market with interest rate r=0.15 (15%) per period. She has the opportunity to purchase a private asset for price P. If she purchases the asset, she will be able to invest any amount z => 0 in this asset. If she invests z => 0 now, the asset will return R(z)=250*z next period.

What is the largest amount P that Anna would be willing to pay for the private asset? (Hint what is the net present value, NPV(z) of the private investment opportunity? What is the optimal investment z& that maximizes NPV(z)?