Question

Rajiv lend out rs 9 to Anni on condition that the amount is payable in 10 months by 10 equal installments of rs. 1 each payable at the start of every month.what is the rate of interest per annum , if the first installment has to be paid one month from the date the loan is availed?

Answer 1

books answer \(\Large 2.222\%\)

Answer 2

it should be way more than 10% right ?
because 1 is more than 10% of 9

Answer 3

http://prntscr.com/5myr2w

Answer 4

i cant understand the book's answer

Answer 5

I don't get the textbook solution either. Here is my attempt :

Suppose the monthly interest rate = \(i\)
Balance after \(1\) month = \(9(1+i) - 1\)
Balance after \(2\) months = \([9(1+i) - 1](1+i)-1 = 9(1+i)^2 - (1+i)-1\)

\(\cdots\)

Balance after \(10\) months = \( 9(1+i)^{10} - (1+i)^9-\cdots -1\)

Answer 6

we want the balance after 10 months to be 0 as the loan gets completely paid off by then :

\( 9(1+i)^{10} - (1+i)^9-\cdots -1 = 0\)

\( 9(1+i)^{10} = (1+i)^9+\cdots +1 \)

right hand side is a geometric series, so we can use the partial sum formula

Answer 7

for the right hand side, there are 10 terms, first term = 1 and common ratio = 1+i so we get

\(9(1+i)^{10} = \dfrac{(1+i)^{10} - 1}{(1+i)-1}\)

\(9(1+i)^{10} = \dfrac{(1+i)^{10} - 1}{i}\)

we can solve \(i\) i guess

Answer 8

solving we get the monthly interest rate \(i = 0.01963\)

http://www.wolframalpha.com/input/?i=solve+9%281%2Bi%29%5E%7B10%7D+%3D+%5Cdfrac%7B%281%2Bi%29%5E%7B10%7D+-+1%7D%7Bi%7D+over+reals&a=i_Variable

Answer 9

multiply \(i\) by 12 for the annual interest rate
\(r = 12i = 12(0.01963) = 0.23556 = 23.556\%\)

Answer 10

answer should be 23.556%

2.222% doesnt make sense to me :O

Answer 11

oh ok, thnx