Question

what is the difference between the compound interest on rs5000 for 3/2 years at 4% per annum compounded yearly and half-yearly ?​

Answer 1

Answer:

What is the difference between the compound interest on rs5000

1/2

years at 4%per annum compounded yearly and half_yearly?(a)Rs 2.04 (b)Rs 3.06 (c)Rs 4.80 (d)Rs 8.30

Answer 2

Answer :-

Given :-

• Sum = Rs. 5000
• Time = 3/2 = 1.5 years
• Rate of interest = 4% p.a.

To find :-

• Difference between compound interest compounded yearly and half-yearly

Solution :-

Compound interest compounded yearly :-

$\sf A = P \Big( 1 + \frac{R}{100} \Big)^n$

Substituting the values -

⇒ $\sf A = P \Big( 1 + \frac{R}{100} \Big)^{n [integer \: part]} \times \Big( 1 + \frac{R \times n[fraction \: part]}{100} \Big)$

⇒ $\sf A = 5000 \times \Big( 1 + \frac{4}{100}\Big)^1 \times \Big( 1 + \frac{4 \times 0.5}{100}\Big)$

⇒ $\sf A = 5000 \times \frac{104}{100} \times \frac{102}{100}$

⇒ $\sf A = 5304$

Compound interest = Amount - Principal

= Rs. 5304 - 5000

= 304

Compound interest compounded yearly = Rs. 304

Compound interest compounded half-yearly -

$\sf A = P \Big( 1 + \frac{\frac{R}{2}}{100} \Big)^{2n}$

Substituting the values -

⇒ $\sf A = 5000 \times \Big( 1 + \frac{\frac{4}{2}}{100} \Big)^{2(1.5)}$

⇒ $\sf A = 5000 \times \Big( 1 + \frac{2}{100}\Big)^3$

⇒ $\sf A = 5000 \times \Big(\frac{102}{100}\Big)^3$

⇒ $\sf A = \frac{5000 \times (102)^3}{(100)^3}$

⇒ $\sf A = 5306.2$

Compound interest = Amount - Principal

= 5306.2 - 5000

= 306.04

Compound interest compounded half-yearly = Rs. 306.04

Difference in the compound interest = 306.04 - 304

= 2.04

Difference between compound interest compounded yearly and half-yearly = Rs. 2.04