Consider a risk-neutral government-subsidized bank that has an average cost of lending each small loan of $100 to the poor as a function of time

where t is the year. The maximum interest rate that the poor can repay is 120 percent. Compute the duration throughout which the government has to subsidize the bank before it can be self-sustainable. If each year, the bank makes ten thousand small loans, compute the total subsidy.

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t: c=- 500 12