John takes out a 2000 10-year loan with an annual effective interest rate of 20%
ID: 2785626 • Letter: J
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. Give your answer rounded to two decimal places.
DO NOT USE A SPREAD SHEET
Explanation / Answer
The amount of the interest on the loan will be $ 2,000* 10 years *20% = $4,000
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 Payment will be 1023X (adding first interest payment to last)
The loan is $4000
X= $4000/1023 = 3.910068
Therefore,The resulting size of X is 3.91
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