Quetzalcoatl and Tonantzin each take out a 17-year loan of $L. Quetzalcoatl repa
ID: 2639144 • Letter: Q
Question
Quetzalcoatl and Tonantzin each take out a 17-year loan of $L. Quetzalcoatl repays his loan using the amortization method, at an annual effective rate of i. He makes an annual payment of $500 at the end of each year. Tonantzin repays her loan using the sinking fund method. She pays interest annually, also at an annual effective interest rate of i. In addition, Tonantzin makes level annual deposits at the end of each year for 17 years into a sinking fund. The annual effective rate on the sinking fund is 4.62%, and she pays off the loan after 17 years. Tonantzin
Explanation / Answer
Tonantzin pays (0.1)L ? iL to the sinking fund each years. The value of sinking fund
accumulates to 10000 in 17 years at 4.62%. So, L = (0.1 ? i)Ls17??|0.0462 and 1/0.1?i =s17??|0.0462 = 25.0003. So, i = 6%. For Quetzalcoatl, L = 500a17??|0.06 = 5238.63.
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