Question

If the amount after 2 years on a certain sum is ₹ 4452 with 6% and 5% p.a. for 2 successive years CI, find the sum.

Answer 1

To find the principal sum when the compound interest rates are given for successive years, we can use the formula for compound interest.

The amount after 2 years can be calculated using the formula:

`A = P(1 + r_1/100)(1 + r_2/100)`

where:

A is the amount after 2 years,

P is the principal amount the sum we want to find, 

r₁ is the interest rate for the first year,

r₂ is the interest rate for the second year.

In this case, A = 4452, r₁ = 6 and r₂ = 5.

Step 1: Set up the equation using the compound interest formula:

`4452 = P(1 + 6/100)(1 + 5/100)`

Step 2: Calculate the factors:

For the first year: `1 + 6/100 = 1.06`

For the second year: `1 + 5/100 = 1.05`

So, the equation becomes 4452 = P × 1.06 × 1.05

Step 3: Calculate 1.06 × 1.05:

1.06 × 1.05 = 1.113

Step 4: Now substitute back into the equation:

4452 = P × 1.113

Step 5: Solve for P:

`P = 4452/1.113`

Step 6: Calculate the value of P:

P ≈ 4000.36

The sum principal amount is approximately 4000.36 rupees.