Question

rohit invests rs.25000 in an investment at a compound interest of 15% per annum.however he has to withdraw his investments after 16 months.how much interest did rohit earn

Answer 1

First, Let us find the Amount Rohit gets After One Year of Investment

We know that : Amount in Compound Interest is given by :

$\clubsuit$  $Amount = P(1 + \frac{R}{100})^n$

Where :

$\spadesuit$  P is the Principal

$\spadesuit$  R is the Rate of Interest

$\spadesuit$  n is the Total Number of Conversion Periods

Here : Principal (P) = 25000 and Rate of Interest (R) = 15 and n = 1 , Because we are Compounding Annually and Calculating Amount after One Year of Investment.

⇒ $A = 25000(1 + \frac{15}{100})^1$

⇒ A = 25000(1 + 0.15)

⇒ A = 25000 + (250 × 15)

⇒ A = 25000 + 3750

⇒ A = 28750

⇒ Rohit gets Rs. 28750 after 12 Months of his Investment

But, the Question is How much Interest did Rohit Earn after 16 Months

Let us Calculate the Simple Interest, he gets with the Amount of Rs.28750 after 4 Months

We know that Simple Interest is given by :

$\clubsuit$  $I = \frac{PTR}{100}$

Here : Time Period(T) = 4 Months = $[\frac{4}{12} = \frac{1}{3}\;Year]$

Here : Principal (P) = 28750 and Rate of Interest (R) = 15

⇒ $Simple\;Interest = (\frac{28750\times \frac{1}{3} \times 15 }{100}) = 1437.5\;Rs$

⇒ The Amount Rohit Receives after 16 Months :

⇒ (28570 + 1437.5) = 30007.5 Rs

⇒ Interest Rohit Earns after 16 Months of Investment :

⇒ (30007.5 - 25000) = 5007.5 Rs

⇒ Interest Rohit Earns after 16 Months of Investment = 5007.5 Rs

Answer 2

Rohit has invested 25000 at a compound interest rate of 15% per annum for 2 years.

However, he withdrew the amount after 16 months.

Therefore following the formula of calculating compound interest we can write 25000(1+15/100) ^16/24 = 27441.33.

Therefore during these 16 months, Rohit had earned interest amount of 27441.33-25000 = 2441.33.