John takes out a 2000 10-year loan with an annual effective interest rate of 20%

Question

John takes out a 2000 10-year loan with an annual effective interest rate of 20%. The principal amount of the loan will be repaid with 10 equal size yearly payments made at the end of each year. The interest accrued on the loan will be repaid with yearly payments occurring at the end of each year. The first interest payment is for X and each subsequent interest payment will be twice as large as the previous interest payment. After 10 years, the loan and interest accrued are completely paid off. Note: The resulting size of X will result in a capitalization of interest on this loan. Find X.

Explanation / Answer

All Amounts in $ The amount of the interest on the loan will be $ 2,000 X 10 years X 20% = 4000 The first interest payment is X The second will be 2X The third will be 4X The fourth will be 8X The fifth will be 16X The sixth will be 32X The seventh will be 64X The eighth will be 128X The ninth will be 256X The tenth will be 512X The total interest will be 1023 X = $ 4,000 Hence, X= $ 4,000 / $ 1,023 = 3.910068 $

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