Question

An amount of Rs. 12820 due 3 years hence, is fully repaid in three annual installments staring after 1 year. The first second and third installments are in ratio 1:2:3. If the rate of compound interest is 10% per annum, find the first installment

Answer 1

a. 2400
b. 1800
c. 2000
d. 2500

Answer 2

it has straight forward solution of

\(\large\tt \begin{align} \color{black}{

a(1.1^²) + 2a(1.1) + 3a = 12820 \hspace{.33em}\\~\\
}\end{align}\)

Answer 3

still looks strange to me

Answer 4

@freckles

Answer 5

@ganeshie8

Answer 6

*

Answer 7

https://www.wolframalpha.com/input/?i=x%281.1%5E2%29+%2B+2x%281.1%29+%2B+3x+%3D+12820

Answer 8

its \(\huge a\)

Answer 9

and you squared that one 1.1 because we were in the third year

Answer 10

I could be completing wrong but your equation seems fine to me

Answer 11

completely*

Answer 12

still feeling stuck on this @mathmath333 ?

Answer 13

yes still stuck @ganeshie8

Answer 14

a sum of 8000 is borrowed at 5% p.a. compound interest and paid back in 3 equal annual instalments .what is the amount of each installment?\(\large\tt \begin{align} \color{black}{\dfrac{x}{(1+\dfrac{5}{100})^1}+\dfrac{x}{(1+\dfrac{5}{100})^2}+\dfrac{x}{(1+\dfrac{5}{100})^3}=8000 \hspace{.33em}\\~\\ }\end{align}\)




for the \(\Huge \uparrow\)

question the rate % is in denominator while for the posted question it is in nummerator

Answer 15

did you watch the movie back to the future

Answer 16

In the first question the debt is due in future

In the second question, you took the loan already so the debt is due from today!

Answer 17

First question is exactly same as below :

find the FUTURE VALUE of money if you make payments each year. first year an amount of \(a\), second year an amount of \(2a\) and in the third year an amount of \(3a\)

Answer 18

assuming payments are made at the end of each year, notice that the first payment stays in bank for exactly 2 years and the interest compounds 2 times :

so the FUTURE VALUE of first payment of \(a\) would be : \(a(1+\frac{10}{100})^2 = a(1.1)^2\)

Answer 19

in the first question \(12820\) is compounded amount or the principle

Answer 20

12820 is the compounded FUTURE amount !
there is no starting principal in the first question

Answer 21

ohk i get that future value formula

Answer 22

oh lol i was assuming it as the principle haha

Answer 23

it was clearly stated as " \(\bf amount\) "of Rs \(12820\) still i was beaten

Answer 24

Ahh I see... that first question is equivalent to the problem of finding the FUTURE VALUE of a savings account where the payments are made at regular intervals.

each payment earns a different interest because of the time value of money

Answer 25

a $100 TODAY is worth more than $1000 after 10 years

Answer 26

so in the previously derived formula it should

\(\large\tt \begin{align} \color{black}{x+\left(x+\dfrac{x\times r\%\times 1}{100}\right)+\left(x+\dfrac{x\times r\%\times 2}{100}\right)\\\cdot \cdot \cdot \cdot \cdot \left(x+\dfrac{x\times r\%\times (n-1)}{100}\right) =\cancel P~~\color{red }{A}\hspace{.33em}\\~\\ }\end{align}\)

Answer 27

it should \(A\) not \(P\)

Answer 28

thats right!

Answer 29

also for this one

\(\large\tt \begin{align} \color{black}{\dfrac{x}{(1+\dfrac{r}{100})^1}+\dfrac{x}{(1+\dfrac{r}{100})^2}\\+\cdot \cdot \cdot \cdot \cdot \cdot \dfrac{x}{(1+\dfrac{r}{100})^n}=\cancel P \color{blue}{A} \hspace{.33em}\\~\\ }\end{align}\)

Answer 30

Looks good!
in the first question you will be `earning` interest because it is same as saving money in your bank.

in the second question you will be `paying` the interest to bank because you took the loan today.

Answer 31

ohk that helps now

Answer 32

thanks!