Question

In how many years will a sum of ₹ 14580 earn ₹ 5420 as CI at `11 1/9`% p.a., compounded annually?

Answer 1

Given:

• Principal P = ₹ 14,580 
• Compound Interest (CI) = ₹ 5,420
• Rate r = `11 1/9% = 100/9%`

Step 1: Total amount A:

A = P + CI

= 14,580 + 5,420

= 20,000

Step 2: Compound Interest: 

`A = P(1 + r/100)^n`

Substitute the values:

`20,000 = 14,580(1 + (100//9)/100)^n`

`20,000 = 14,580(1 + 1/9)^n`

`20,000 = 14,580(10/9)^n`

Step 3: Solve for `(10/9)^n`:

`(20,000)/(14,580) = (10/9)^n`

`1.3717 ≈ (10/9)^n`

Step 4: Express as a fraction for exact calculation:

`(20,000)/(14,580) = 20000/14580`

= `(20000 ÷ 20)/(14580 ÷ 20)`

= `1000/729`

So, `(10/9)^n = 1000/729`

Step 5: Recognize powers:

`1000/729 = 10^3/9^3 = (10/9)^3`

∴ n = 3 years