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 : 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)³X(1.1)¹⁰

598.74 = X (0.6144567106)        

              (1.1) 0.09090909

X = 97.44

c.

step-by-step explanation:

because first you have to add the 4x, 9x, and the 7x together and you get 20x and then you add the last numbers up and you get 5and then you put the subtraction sign in there and that's how you get the answer.

where is the option given