Question

The compound interest on half-yearly rests on Rs. 10,000 the rate for the first and second years being

6% and for the third year 9% p.a. is

(a) Rs.2,200

(b) Rs.2,287

(c) Rs. 2,285

(d) Rs.2290.84​

Answer 1

Question:

The compound interest on half-yearly rests on Rs. 10,000 the rate for the first and second years being 6% and for the third year 9% p.a. is ?

Explanation:

Solution:

Principle = p = 10,000

Rate of interest for the first an second year is 2% and for the third year is 9%Question:

Let us find the interest for 2 years

We know

$\boxed{\sf{\bullet\:{Compound\:Interest = P(1 + I)^n-1}}}$

Lets find out the interest

$\sf{\implies\:{CI = 10,000(1 + \dfrac{0.06}{2})^4-1}}$

$\sf{\implies{CI = 10,000(1+0.03)^4-1}}$

$\sf{\implies{CI = 10,000(1.03)^4-1}}$

$\sf{\implies{CI = 10,000\:x\:0.12550881}}$

$\sf{\implies{CI = 1,255}}$

Amount at the begining of third year is;

$\boxed{\sf{\bullet\:{Amount = Principle + Compound\:Interest}}}$

$\sf{\implies{Amount = 10,000 + 1,255}}$

$\sf{\implies{Amount =\underline{\underline{ 11,255}}}}$

Interest for the third year;

$\sf{\implies\:{CI = 11,255(1 + \dfrac{0.09}{2})^2-1}}$

$\sf{\implies{CI = 11,255(1+0.045)^2-1}}$

$\sf{\implies{CI = 11,255(1.045)^2-1}}$

$\sf{\implies{CI = 11,255\:x\:0.092025}}$

$\sf{\implies{CI = 1,036}}$

Amount at the end of third year is 11,255 + 1,036 = 12,291