Question

Anshika invests ₹ 5000 compounded yearly. At the end of one year, it amounts to ₹ 5200. Calculate

1. the rate of interest
2. the CI for the second year

Answer 1

Given:

• Principal (P) = ₹ 5,000
• Amount after one year (A₁) = ₹ 5,200
• Time (n) = 1 year for the first year and 2 years in total,

i. Rate of interest (R):

We can use the compound interest formula for the first year to calculate the rate of interest:

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

For the first year:

`A_1 = P(1 + R/100)`

Substitute the given values:

`5,200 = 5,000(1 + R/100)`

Now, solve for R:

`(5,200)/(5,000) = 1 + R/100`

⇒ `1.04 = 1 + R/100`

⇒ `R/100 = 0.04`

⇒ R = 4%

So, the rate of interest is 4%.

ii. Compound interest for the second year (CI for 2nd year):

To calculate the compound interest for the second year, we first find the amount at the end of the second year using the compound interest formula:

`A_2 = P(1 + R/100)^2`

Substitute the given values:

`A_2 = 5,000(1 + 4/100)^2`

= 5,000 × 1.04²

= 5,000 × 1.0816

= 5,408

Now, to find the compound interest for the second year, subtract the amount at the end of the first year from the amount at the end of the second year:

CI = A₂ – A₁

= 5,408 – 5,200

= ₹ 208

So, the compound interest for the second year is ₹ 208.