Question

At what rate of compound interest per annum will a sum of Rs.10,000 becomes

Rs.14641 in 4 years?​

Answer 1

Answer:

I have done in three ways

Step-by-step explanation:

Solution:

Given,

Sum = Rs. 10000

Amount = Rs. 14641

Rate = 20% per annum = 10% per 6 month

Now,

Amount = Principal{1 + (rate/100)}time

⇒ 14641 = 10000{1 + (10/100)}time

⇒ 14641/10000 = (11/10)time

⇒ (11/10)4 = (11/10)time

⇒ time = 4

AS, it was compounded half yearly

∴ Actual time of investment = 4/2 = 2 years

 

                                                            OR

Given,

Sum = Rs. 10000

Amount = Rs. 14641

Rate = 20% per annum = 10% per 6 month

Now,

Compound interest = Principal{1 + (rate/100)}time

⇒ 14641 = 10000{1 + (10/100)}time

⇒ 14641/10000 = (11/10)time

⇒ (11/10)4 = (11/10)time

⇒ time = 4

AS, it was compounded half yearly

∴ Actual time of investment = 4/2 = 2 years

                                                               OR

An amount of Rs. 10000 becomes Rs. 14641 in 2 years if the interest is compounded half yearly. What is the rate of compound interest p.c.p.a. ?

A. 10%

B. 12%

C. 16%

D. 20%

E. None of these

Answer: Option D

Solution=

Let the rate be R% p.a.

Then,10000(1+R2×100)4=14641

⇒(1+R200)4=1464110000=(1110)4

⇒1+R200=1110

⇒R200=110

⇒R=20%