Question

pooja started a business by investing rs 200000 .during the first three successive years she earns a profit of 5% ,8% and 12% p.a respectively. if in each year the profit was added on the capital atvthe end of ptevious year, calculate her total profit.

Answer 1

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We first assign a variable to Pooja's initial investment, say, P_i.

Basically, here's the steps on what we need to do:
-In the first year, add Pooja's profit after that year
-Use this value to as new base amount for growth next year, then add the profit
-Continue until the number of years we desire.

We first designate the value of the investment after each year

I_1, for investment at year 1
I_2, for investment at year 2
I_3, for investment at year 3

...

and so on, so carrying on..

if our capital is I_0, then the profit for year 1, taking 5% as profit, will be

I_1 = I_0 + (0.05)I_0 = 200,000 + (0.05)200,000 = 210,000

for year 2, having 8% profit

I_2 = I_1 + (0.08)I_1 = 210,000 + (0.08)210,000 = 226,800

for year 3, having 12% profit

I_3 = I_2 + (0.12)I_2 = 226,800 + (0.12)226,800 = 254,016

and we can repeat this process if we know the percent increase in profit. However, since we only want to know the profit after three years, we can stop here so:

Pooja's investment will be ₹254,016 after 3 years.