Question

Hey guys please help me out..
"The compound interest,calculated yearly on a certain sum of money for the second year is Rs. 880 and for the third year it is Rs.968. Calculate the rate of interest and the sum of money.. Administrators...please help..

Answer 1

Can you please show me the working which mifht help me to understand... Then i can clear my doubts and have a clear concept @campbell_st!!!! Pl help..

Answer 2

Um.. Actually i dont think the time period is 1year. Because i mentioned in the question that 880 is theC.I. For the 2nd year so i guess the time is 2years? @campbell_st

Answer 3

Oh well i'll try and let you know in a bit... Thank you so much..

Answer 4

Well @campbell_st thank u sooo.... Much... The answer is 11% right? Just confirm...

Answer 5

Yea... I'm sorry dat ws a typing error its 10% but they've asked us to find the sum of money as well so how would i do that? @campbell_st

Answer 6

Well is the answer 8000?

Answer 7

@campbell_st?

Answer 8

But according to my book it iis Rupees 8000... And i didnt understand. Why the C.I for the second year is taken as the principal.. Plz explain ot once again...

Answer 9

@campbell_st??!

Answer 10

Yea... Although the rate % is correct..

Answer 11

Okay so theres an equation like P=968000/331? Right?

Answer 12

@campbell_st??

Answer 13

Oh well i'm sorry for disturbing you late at night.. Its morning here though... Anyways thank you so much for helping me till this far....@campbell_st

Answer 14

Can any one else please help? @satellite73

Answer 15

Let the principal = P
Let the annual rate of interest as a decimal = r
The amount at the end of the first year including interest = P(1 + r)
The amount at the end of the second year = P(1 + r) + {(P(1 + r) * r)}
The amount at the end of the third year = P(1 + r) + {(P(1 + r) * r)} + P(1 + r) + [{(P(1 + r) * r)} *r]
We can now form two equations using the given amounts of interest:
{(P(1 + r) * r)} = 880 ......................................(1)
{(P(1 + r) * r)} + {(P * r^2)(1 + r)} = 968 .........(2)
Substituting the value of {(P(1 + r) * r)} obtained in equation (1) into equation (2) gives
{(P * r^2)(1 + r)} = 88
which gives
\[P=\frac{88}{r ^{2}(1+r)}\ ....................(3)\]
Substituting the value for P obtained in equation (3) into equation (1) we get
\[\frac{88r}{r ^{2}}=880\]
\[\frac{88}{r}=880\]
r = 0.1
Substituting this value for r into equation (1) we find that P = 8000

Answer 16

thank u @kropot72 !!! thanks a zillion..

Answer 17

You're welcome :)

Answer 18

@kropot72 can u say y v need to add d interest in d second year?

Answer 19

@kropot72 ??

Answer 20

The interest is added at the end of the second year:
The amount at the end of the second year = P(1 + r) + {(P(1 + r) * r)}
the interest being {(P(1 + r) * r)}

Answer 21

still dont get it!

Answer 22

@kropot72 ???

Answer 23

The amount at the end of the first year including interest = P(1 + r)
Do you understand the above?

Answer 24

yes.. proceed..

Answer 25

The interest for the second year is calculated on the amount at the end of the first year.
The amount at the end of the first year including interest = P(1 + r)
The interest on P(1 + r) for a year is {(P(1 + r) * r)}
being the amount at the end of the first year multiplied by the interest rate.

Answer 26

oh... thanks....now i got it.. thank u and gudni8! @kropot72

Answer 27

You're welcome :)