0, John takes out a 2000 10-year loan with an annual effective interest rate of
ID: 2786439 • Letter: 0
Question
0, 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. PYM T-PR + INT 20% PR= .Explanation / Answer
The present value of the loan is $2000
This should be equal to the present value of interest payments + present value of principal payments
Principal payment = 2000/10 = $200
PV of principal payments = 200*(1-1.2^-10)/0.2 = 838.4944
Interest is growing @ 100%, r=20%
Using the growing annuity formula,
X/ (r-g) * (1- (1+g/ 1+r)^n)
Hence
(X/ -0.8 )* (1- (2/1.2)^10)
= 205.477 X
Thus the PV equation is
2000 = 205.477X+ 838.4944
1161.506 = 205.477X
X= $5.65
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