Question

Compound Interest compounded quarterly on Rs. 15000 for 3 years is Rs. 986 more than

Simple Interest on the same principal for 3 years. Find the rate of interest.​

Answer 1

The rate of interest is 12%

• Let the rate of interest be r. Now given principal amount Rs. 15000 and time 3 years which is compounded quarterly
• So the compound interest generated is 15000(1+r/400)^(4*3) - 15000 = 15000(1+r/400)^12 - 15000
• Now the simple interest on the same principal for three year is 15000*r*3/100 = 450r
• Now it is given that 450r + 986 = 15000[(1+r/400)^12 - 1)]
• Now solving this equation we get  r equal to approximately as 12
• Hence the rate of interest is 12%

Answer 2

Answer:

Compound Interest compounded quarterly on Rs. 15000 for 3 years is Rs. 986 more than  Simple Interest on the same principal for 3 years. The rate is 12%

Step-by-step explanation:

Let r be rate of interest.

Since the amount is compounded quarterly, we have that:

n = 3 × 4 = 12 periods

rate = r/4

The accumulation formula is given as:

A = P(1 + r/4)¹²

Substituting the values we have:

A = 15000 (1 + r/4)¹²

Interest = 15000(1 + r/4)¹² - 15000

The simple interest i given by:

Simple interest = 15000 × r/100 × 3 = 450r

The difference is 986.

Let's write this below:

986 = [15000(1 + r/100)¹² - 15000] - 450r

986 + 15000 = 15000(1 + r/100)¹² - 450r

15986/15000 = (1 + r/4)¹² - 450r/15000

1.0657 = (1 + r/4)¹² - 0.03r

We need to use trial and error to solve this.

Let's assume r = 5%

Substituting we have:

1.0657 = 1.16075 - 0.015

1.0657 = 1.14575

RHS is not equal to LHS. So, 5% is not the rate.

Let's assume the rate is 10%

1.0657 = 1.34489 - 0.3

1.0657 = 1.04489

Let's assume the rate is 12%

1.0657 = 1.4258 - 0.36

1.0657 = 1.0658

The LHS is approximately equal to the RHS. So, the rate of interest is 12%