Fred needs to take out a loan but doesn't know exactly how much money he needs...

 

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Fred needs to take out a loan but doesn't know exactly how much money he needs to borrow yet. He knows that if he does take out a loan, he'll have to pay simple interest on it, where for every month he doesn't pay it back, the amount he has to pay back goes up by 5% (even if he doesn't borrow it for a full month, he'll still have to pay back the original amount he borrowed.) Note: Money Fred has to pay back after t months = A; A = P*(1 + rt) where r is the interest rate, P is the initial amount he borrowed Fred does know two things though: He knows he needs to borrow the money for exactly 1 year, and that he wants the amount of money he borrows to be 0.625 times the amount he ends up having to pay back. (Fred's mind works in mysterious ways...) How much money should Fred borrow to ensure this? Can he borrow any amount, one particular amount, or no amount, and how do you know? Fred needs to take out a loan but doesn't know exactly how much money he needs to borrow yet. He knows that if he does take out a loan, he'll have to pay simple interest on it, where for every month he doesn't pay it back, the amount he has to pay back goes up by 5% (even if he doesn't borrow it for a full month, he'll still have to pay back the original amount he borrowed.) Note: Money Fred has to pay back after t months = A; A = P*(1 + rt) where r is the interest rate, P is the initial amount he borrowed Fred does know two things though: He knows he needs to borrow the money for exactly 1 year, and that he wants the amount of money he borrows to be 0.625 times the amount he ends up having to pay back. (Fred's mind works in mysterious ways...) How much money should Fred borrow to ensure this? Can he borrow any amount, one particular amount, or no amount, and how do you know?

Answer rating: 100% (QA)

Fred should borrow no more than 625 If he borrows any more money than that h... View the full answer