Question

If simple interest for 2 years for a sum is rs.600 and compound interest for the same sum for 2 years and same rate of interest is rs.645,what will be the rate of interest?

Answer 1

Answer:

15

Step-by-step explanation:

imagine that the principal sum is 'P' and rate of interest is 'r'

in first case

P×r×2/100=600

or, Pr=30000

in second situation

P(1+r/100) square - P=645

or, P(1+r/50+r×r/10000-1)=645

or, Pr/50+Pr×r/10000=645

or, 30000/50+30000×r/10000=645

or, 600+3r=645

or, 3r=45

or, r=15

Answer 2

Given: The simple interest for 2 years for a sum = Rs. 600

The compound interest for the same sum for 2 years at the same rate of interest = Rs. 645

To find: The rate of interest

Solution: The simple interest is given by the formula:

S.I = (P × r × t)/100 [where P is the sum of money, r is the rate of interest, and t is the time period].

Here, S.I = Rs. 600 and t = 2 years.

Hence according to the question,

600 = (P × r × 2)/100

⇒ P  × r = (600 × 100)/2

⇒ Pr = 30000

The compound interest is given by the formula:

C.I = P(1 + r/100)^n - P [where n is the time period]

Here, C.I = Rs. 645 and n = 2 years.

Now according to the question,

645 = P(1 + r/100)² - P

⇒ 645 = P{(1 + r/100)² - 1}

⇒ 645 = P{1 + 2r/100 + r²/10000 - 1}

⇒ 645 = P{2r/100 + r²/10000}

⇒ 645 = Pr{1/50 + r/10000}

⇒ 645 = 30000{1/50 + r/10000}

⇒ 1/50 + r/10000 = 645/30000

⇒ r/10000 = (645 - 600)/30000

⇒ r = (45 × 100000)/30000

⇒ r = 45/3

⇒ r = 15 %

Therefore, the rate of interest is 15%.

Answer: 15%