Question

A money lender borrows some money at 4% per annum and pays the interest at the end of the year. He lends it at 6% p.a. compounded half-yearly and receives the interest at the end of the year. In this way he gains Rs.104.50 during the year. How much money does he borrow?

Answer 1

lets say he borrowed \(x\) dollars

Answer 2

x*4*1/100-x(1+6/2/100)=104.50

Answer 3

very good try ! keep in mind : `compounded half-yearly` means, n = 2, right ?

Answer 4

yes so only rate of interest =6/2 and time =2 yrs but didnt put that one

Answer 5

interest paid = 4% of x = \(\large \dfrac{4}{100}x\)
interest earned = 6% compounded half yearly = \(\large x\left(1+\dfrac{0.06}{2}\right)^2 - x\)

Answer 6

subtracting above both interests gives you the profit earned

Answer 7

Profit = \[\large x\left(1+\dfrac{0.06}{2}\right)^2 - x - \large \dfrac{4}{100}x\]

Answer 8

set it equal to 104.50 and solve x

Answer 9

3.2036x=104.50
so x=32.069

Answer 10

try again

Answer 11

x=32.65

Answer 12

4.2406x-x-0.04

Answer 13

check ur calculation for first term : \(\large x\left(1+\dfrac{0.06}{2}\right)^2\)

Answer 14

http://www.wolframalpha.com/input/?i=+x%281%2B%5Cdfrac%7B0.06%7D%7B2%7D%29%5E2

Answer 15

oh i made a mistake by not dividing it by 2 ya

Answer 16

2.06*2.06 frankly i wrote

Answer 17

okay, so what do you get for x ?

Answer 18

94.97 something is it right?

Answer 19

nope, try again

Answer 20

0.0209x

Answer 21

5000

Answer 22

\[\large x\left(1+\dfrac{0.06}{2}\right)^2 - x - \large \dfrac{4}{100}x\]

\[\large 1.0609x - x - 0.04x\]

\[\large 0.0209x\]

Answer 23

so 5000

Answer 24

yes, setting it equal to 104.50 and solving x gives you x = 5000 !