Question

If the compound interest for a certain sum for 2 years is 21.what could be the simple interest?
a. 20
b. 16
c. 18
d. 20.5

Answer 1

@Michele_Laino

Answer 2

ermm i got a formula by googeling :P
my brain crashed so i'll just post it without checking if its right or not :P (Hope its help)

Answer 3

nvm i have no clue :3

@hartnn

Answer 4

\(\large \tt \begin{align} \color{black}{21=p\left(1+\dfrac{n}{100}\right )^2-p\\~\\
\normalsize \text{now i want to find}\\~\\
\dfrac{p\times n\times 2}{100}=?

}\end{align}\)

Answer 5

@Marki

Answer 6

looks like you have to isolate p from 1st equation and plug it in 2nd equation to get an equation in only n

Answer 7

yes its very painful ,

Answer 8

but their must be a trick

Answer 9

to simplify a bit, keep n/100 as say N

Answer 10

p = 21/(N^2+2N)
not so bad

Answer 11

you need
42N/(N^2+2N) = 42/(N+2)

Answer 12

how did u get the above ^

Answer 13

n/100 = N

21 = p [1+2N+N^2-1]

Answer 14

yes i got that

but how u got

that 42N stuff

Answer 15

you need
2pN right?

2N times p
2n times 21/[N^2+2N]

Answer 16

oh i see ,lol

Answer 17

but we don't know the rate of interest

Answer 18

i'll say keep p =100
find N

use this p and N in SI formula

Answer 19

even better, keep p =21 :P

Answer 20

yes but why assuming p=100

Answer 21

we have one equation and 2 unknowns

Answer 22

oh i see the trial and error

Answer 23

for \(p=21\)
i got

\((N+1)^2=2\)

how to proceed further

Answer 24

still stuck ?

Answer 25

:( yes

Answer 26

this question beats me , i think its somewhat lacking information or either wrong

Answer 27

with p =21
i get SI = 17.38 ...

Answer 28

the question clearly ask "what could be the simple interest"
so there is no single answer, we need to try each option i guess

Answer 29

\(21=p\left(1+\dfrac{r}{100}\right )^2-p\)

suppose the interest rate is 100%
then \(21 = p(1+1)^2 -p \implies p = 7\)

that gives you simple interest = \(14\)

so 100% is too optimistic

Answer 30

lets try interest rate = 10%, then you get
\(21 = p(1+0.1)^2-p \implies p = 100\)

that gives you simple interest = \(20\)

which is one of your options! so you're done!

Answer 31

how will my mind think that i have to put
\(r=10\%\)

Answer 32

with some other interest rate, we could get 16 or 18 ...

Answer 33

lets try and see if its really possible..

Answer 34

yes it does work for \(p=100\)

Answer 35

20%, 19
25% , 18.66,
30% ,18.25

Answer 36

http://www.wolframalpha.com/input/?i=solve+p%281%2B%5Cdfrac%7Bn%7D%7B100%7D%29%5E2-p%3D21+%2C+2*p*%28n%2F100%29%3D18

Answer 37

try p = 12.8 and r = 62.5%
you will get simple interest = 16 and compound interest = 21

Answer 38

so is this question wrong

Answer 39

i guess so

Answer 40

but you will need to do ponder on this some more before concluding the question is wrong