Assume the annual profit from a credit$-$card customer is year $1$ $$100,$ year $2$ $$125,$ year $3$ $$150,$ year $4$ $$150,$ year $5,$ $$150,$ year $6$ $$200,$ year $7$ $$250.$

Each year there is a $50\%$ chance of keeping the customer and the discount rate is $25\%.$

What is the present value of this customer over the next seven years?