Investement and financial planning - class-IX

Investments in Equity Linked Saving Schemes or ELSS qualify for tax deduction under Section $80C$ of the Income Tax Act. The maximum tax deduction allowed under Section $80C$ is Rs 1.5 lakh under Section $80C$.

$F=C.F. (1+i)^n$
Where, $F=$ Future value
$C.F. =$ Cash flow $=$Rs. $3,000$
$i=$ rate of interest $=0.12$
$n=$ time period $=2$
$F=$Rs. $3,000(1+0.12)^2$
$=$Rs. $3,000\times 1.2544$
$=$Rs. $3,763.20$

Systematic Investment Plan (SIP) is an investment vehicle offered by mutual funds to investors, allowing them to invest small amounts periodically instead of lump sums.
It is good for investors who don't have much financial market's understanding.
It involves lesser risks and low returns because investment is done in small amounts over a period of time.

Year 1: 4000 * 1.1 = 4400; 4400 - 1000 = 3400. Year 2: 3400 * 1.1 = 3740; 3740 - 1000 = 2740. Year 3: 2740 * 1.1 = 3014; 3014 - 1000 = 2014.

Mutual Fund is a professionally managed investment scheme, which is run by AMC. Mutual Fund is a mediator that brings together a group of people and invests 'their' money in stocks, bonds and other securities.

The question is complex and often appears in competitive exams with specific annuity formulas. Given the structure of 20 installments of 1000, the final payment must account for the remaining principal and interest.

Let Ajay's investment be x and his time be 12 months. Anil's investment is x + 300 and his time is 6 months. Ratio of their profits: Ajay's share = Rs. (200 + 25) = Rs. 200, Anil's share = Rs. (200 - 25) = Rs. 175 since total profit is 375 and Ajay got 25 more than Anil. Ratio of profits = Ajay / Anil = 200 / 175 = 8 / 7. Also, ratio of profits equals ratio of (investment * time): (x * 12) / ((x + 300) * 6) = 2x / (x + 300). Equating these gives 2x / (x + 300) = 8 / 7, meaning 14x = 8x + 2400, so 6x = 2400, x = 400. Anil's investment is x + 300 = 700.

Let p invested Rs x Then q invested Rs $(27000-x)$
$\therefore x(1+\dfrac{8}{100})^{2}-1+(27000-x)(1+\dfrac{9}{100})^{2}-1=4818.30$
$\Rightarrow (x\times \dfrac{104}{625})+\dfrac{1881(27000-x)}{10000}= \dfrac{481830}{100}$
$\Rightarrow 1664x+1881(27000-x)=48183000$
$\Rightarrow (1881x-1664x)=50787000-48183000$
 Or $217x=2604000$
  Or $x=12000 Rs$

Total cost =$ 400
Down payment=$ 75
Remaining amount=$400-75=$ 325$
Balanced paid in 24 months=$23 \times 16+9=$ 377$
Difference=$377-325=$52$
The per cent of interest to the borrowed sum=$\frac{52}{325}\times 100=16$

Total investment by A=$500+1500=2000$
Yearly return =8.5 % of 2000
$\Rightarrow \frac{8.5}{100}\times2000=170$
Yearly return of 500=7% of 500
$\Rightarrow \frac{7}{100}\times500=35$
Let yearly return of 1500 is x
Yearly return=x% of 1500
$\Rightarrow \frac{x}{100}\times 1500=15x$
Then according to the question
$\Rightarrow 35+15x=170$
$\Rightarrow 15x=170-35$
$\Rightarrow 15x=135$
$\Rightarrow x=\frac{135}{15}=9$
                     

Given  person pays $400$ every as loan installments to bank

Amount of one year

$\displaystyle=200\left[1+\frac{5}{100}\right]$

$\displaystyle=200\times\frac{21}{20}=210$

$\therefore$ At the end of year he pays back Rs. 50. So the principal for the second year is Rs. 160.
$\therefore$ Amount of Second year

$\displaystyle=160\left[1+\frac{5}{100}\right]$

$\displaystyle=160\times\frac{21}{20}=168$

$\therefore$ At the end of year he pays back Rs. 50. 
So rest amount = 168 -50 = Rs. 118.
This amount is principal amount for third year.
$\therefore$ Amount of third year

$\displaystyle=118\left[1+\frac{5}{100}\right]$

$\displaystyle=118\times\frac{21}{20}=123.90$

At the end of years he pays back Rs. 50.
So rest amount
$=123.90-50=Rs. 73.90$
This amount is principal for fourth year.
$\therefore$ Amount of fourth year

$\displaystyle=73.90\left[1+\frac{5}{100}\right]$

$\displaystyle=73.90\times\frac{21}{20}=77.59$

At the end of year he pays back Rs. 50.
So rest amount
$=77.595-50=Rs. 27.59$
$\therefore$ At the end of fourth year he owes Rs. 27.59.

Interest at $10%$ for the first month for Rs. $20$ lakhs $=$ $2000000 \times \dfrac{1}{12}\times \dfrac{10}{100}=16666.66$
EMI for one month, for $20$ lakhs $= 2500 \times  20 =$ Rs. $50000$
Hence principal repaid $=$ Rs. $50000 - 16666.66 =$ Rs. $33333.34$

Given, $n = 6, I =$ Rs. $1600$, 

r $ = 2\dfrac {1}{2} $ % $ = \dfrac {5}{2} $ % n $ = 18 $ months $ = \dfrac {3}{2} $ years

When the interest is compounded half yearly,

$ A=P\left( 1+\dfrac { r }{ 2\times 100 }  \right) ^{ n\times 2 } $

$ => 9826 = P\left( 1+\dfrac { \dfrac {5}{2} }{ 2\times 100 }  \right) ^{ \dfrac {3}{2}\times 2 } $
$ => 9826 = P( \dfrac {81}{80}) ^{ 3 } $
$ => P =Rs 9466.54 $

Amount required to buy $500$ such units