A man borrows a certain sum at 20% compounded annually and lends it at 25% simple interest. What is the maximum number of years for which he can wait, so that he does not bear any loss?

The amount to be repaid on the borrowed sum after n years is calculated using the compound interest formula as Principal multiplied by 1.2 raised to the power of n. The amount received from lending the same sum at 25 percent simple interest is Principal multiplied by 1 plus 0.25n. To avoid a loss, the lending return must exceed the borrowing debt, so we evaluate the inequalities for consecutive years: for 3 years the return is 1.75P while the debt is 1.728P, securing a profit, but for 4 years the return is 2P while the debt equals 2.0736P, resulting in a loss. The maximum number of years he can wait is 3.

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