Question

Find the difference between the simple interest and the compound interest on 32000 for 1 year at 5% p.a., compound interest being reckoned half yearly

Answer 1

The difference between the simple interest and the compound interest is Rs. 20.

Step-by-step explanation:

Case 1: For Simple Interest

It is given,

Principal, P = Rs. 32000

Rate of interest, R = 5 % p.a.  

Time period, T = 1 year

∴ Simple Interest = $\frac{PRT}{100} = \frac{32000 * 5 * 1}{100}$ = Rs. 1600  

Case 2: For Compound Interest

P = Rs. 32000

Since the interest is compounded half-yearly

R = $\frac{5}{2}$ = 2.5%

T = 2 * 1 = 2 years

A = P (1 + $\frac{R}{100}$)ⁿ

⇒ A = 32000 (1 + $\frac{2.5}{100}$)²

⇒ A = 32000 * $\frac{102.5}{100} * \frac{102.5}{100}$

⇒ A = Rs. 33620

∴ Compound Interest = 33620 - 32000 = Rs. 1620

Thus,

The difference between compound interest and simple interest is given by,

= 1620 - 1600  

= Rs. 20

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Answer 2

Answer:

The difference between the simple interest and the compound interest is Rs. 20.

Step-by-step explanation:

Case 1: For Simple Interest

It is given,

Principal, P = Rs. 32000

Rate of interest, R = 5 % p.a.  

Time period, T = 1 year

∴ Simple Interest = \frac{PRT}{100} = \frac{32000 * 5 * 1}{100}100PRT=10032000∗5∗1 = Rs. 1600  

Case 2: For Compound Interest

P = Rs. 32000

Since the interest is compounded half-yearly

R = \frac{5}{2}25 = 2.5%

T = 2 * 1 = 2 years

A = P (1 + \frac{R}{100}100R )ⁿ

⇒ A = 32000 (1 + \frac{2.5}{100}1002.5 )²

⇒ A = 32000 * \frac{102.5}{100} * \frac{102.5}{100}100102.5∗100102.5

⇒ A = Rs. 33620

∴ Compound Interest = 33620 - 32000 = Rs. 1620

Thus,

The difference between compound interest and simple interest is given by,

= 1620 - 1600  

= Rs. 20