Question

A 20-year loan of 1000 is repaid with payments at the end of each year. Each of the first ten payments equals 150% of the amount of interest due. Each of the last ten payments is X. The lender charges interest at an annual effective rate of 10%. Calculate X.
(A) 32


(B) 57


(C) 70


(D) 97


(E) 117

Answer 1

Answer : X = 97.44

Step-by-step explanation:

Loan of Amount = 1000 to be paid in 20 years

rate of interest = 10%

Year 1 interest due = 0.1 x 1000 = 100

150% of 100 = 150

100 goes into interest, 50 reduce the principal, then principal for 2nd year  = 1000-50 = 950

Year 2 interest due = 0.1 x 950 = 95

150% of 95 = 142.5

95 goes into interest, 47.5 reduce the principal, then principal for 3rd year  = 950 - 47.5 = 902.50

AFTER 10 YEARS THE AMOUNT LEFT =(0.95)¹⁰ X 1000

                                                                          598.74            

Last ten payment = X

598.74 = X/0(1.1) + X/(1.1)² + X(1.1)³............X(1.1)¹⁰

598.74 = X (0.6144567106)        

              (1.1) 0.09090909

X = 97.44