Question

In what period will ₹ 24000 yield ₹ 7944 as compound interest at 10% per annum compounded yearly.

Answer 1

Given:

• Principal (P = ₹ 24000)
• Compound Interest (C.I. = ₹ 7944 )
• Rate of interest (r = 10%) per annum.
• Interest compounded yearly.
• Need to find number of years (n).

Step-wise calculation:

1. Compound interest is given by the formula:

`C.I. = P(1 + r/100)^n - P`

`C.I. = P(1 + r/100)^n - 1`

2. Substitute the known values:

`7944 = 24000(1 + 10/100)^n - 1`

3. Simplify the expression inside the brace:

7944 = 24000((1.1)ⁿ – 1)

4. Divide both sides by 24000:

`7944/24000 = (1.1)^n - 1`

5. Calculate the left side:

0.331 = (1.1)ⁿ – 1

6. Add 1 to both sides:

(1.1)ⁿ = 1.331

7. Taking natural logarithm on both sides:

ln (1.1)ⁿ = ln 1.331

8. Use logarithm power rule:

n ln 1.1 = ln 1.331

9. Find values of logarithms:

ln 1.1 ≈ 0.09531,

ln 1.331 ≈ 0.28650

10. Solve for n: 

`n = 0.28650/0.09531 ≈ 3`

The period (n) for which ₹ 24000 yields ₹ 7944 as compound interest at 10% per annum compounded yearly is approximately 3 years.