BMO administers a mortgage on someone$$s house. That mortgage obligates the homeowner to pay $$50,000$ each year to BMO $($paid in regular, small installments$)$ for the next $25$ years.

BMO would like to sell that mortgage to Scotiabank, so they need to approximate its value in present$-$day dollars.

$($a$)$Assuming a future discounting rate of $10\%($as in the last question$),$ use an integral to approximate the value of the mortgage, in present$-$day dollars. Then, use a calculator to approximate the result to the nearest cent.

$($b$)$Suppose BMO sells the mortgage to Scotiabank for the price you found in part $($a$).$ They put that money into an account earning a fixed interest rate, compounded continuously. No other money is put into the account, or taken out. What interest rate would the account have to earn, in order for the balance to be $$1,250,000$ after $25$ years?

$($$$1,250,000$ is the amount of money BMO would have collected over the life of the mortgage, had they not sold it$.)$

$6/6$Tht