John wishes to borrow 20,000. Lender X and Y offer the following terms: (1) Lender X will be repaid with 15 equal annual payments made at the end of each year at 5% interest effective annually. (2) Lender Y charges an annual effective interest rate of i with John accumulating the amount necessary to repay the loan by means of fifteen annual deposits at the end of each year into a sinking fund earning 4% interest effective annually. (3) The total payment (principal and interest) is the same for lender X as for lender Y. Calculate i.

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Amortized Loans

The term "amortization" refers to spreading the value of a loan or a debt over a series of regular payments or installments comprising of both the principal and interest amount. It generally involves the process where in the value of a loan or an intangible asset is written down over its maturity period.