Question

Primal receives Rs 1489.5 as compound interest at end of three years and Rs 945 at end of two years. Calculate principal amount invested when both interests are compounded annually.

1. Rs 6000
2. Rs 5500
3. Rs 5000
4. Rs 4500

Answer 1

Correct Answer - Option 4 : Rs 4500

 

Calculation:

Assuming principal amount = X and rate of interest = r%

Compound interest at end of two years = (X × (1 + r) ²) – X

⇒ X × (1 + 2r + r²) – X = 945

⇒ X × (r² + 2r) = 5445     ….(1)

Compound interest at end of three years = X × (1 + r)³ – X

⇒ X × (r³ + 1 + 3r² + 3r) – X = 1489.5

⇒ X × (r³ + 3r^r + 3r) = 1489.5    ….(2)

Hence, dividing equation 2 by 1

⇒ (r³ + 3r^r + 3r)/ (r² + 2r) = 1489.5/ 945

⇒ (r² + 3r + 3)/ (r + 2) = 1489.5/ 945

⇒ 945 × r² + 2835r + 2835 = 1489.5r + 2979

⇒ 945 × r² + 1345.5r – 144 = 0

Solving the above equation r = 0.10

⇒ r = 10%

Now, placing value of r in equation 2

⇒ X × ((0.10)² + 0.20) = 945

⇒ X × 0.21 = 945

⇒ X = 4500

∴ Principal amount is Rs 4500