What annual installment will discharge a debt of Rs. 9,600 due in 5 years at 10% simple interest?

Given:

The debt = 9600

Concept:

 SI = P × R × T/100,    Where, SI = The simple interest, P = The principle, R = The rate of interest, and T = The time

Calculation:

Let us assume the annual installment be X

⇒ For first-year installment = 100% of X

⇒ For second-year installment = 110% of X

⇒ For third-year instalment = 120% of X

⇒ For fourth-year instalment = 130% of X

For fifth year installment= 140% of X

⇒ According to the question

⇒ X × (100 + 110 + 120 + 130 + 140)% = 9600

⇒ 600% × X = 9600

⇒ X% = 16

⇒ The annually installment = X = 16 × 100 = 1600

∴ The required result will be 1600.

Shortcut Trick

The annual installment discharge dept of P due in t years at r% S.I ⇒ \(\frac{P \times 100}{t \times 100 + (t_{n-1} + t_{n-2} + .. + 1)\times r}\) 

So, according to the question, P = 9600, t = 5 and r = 10%

⇒ \(\frac{9600 \times 100}{5\times 100 + (4 + 3 + 2 + 1)\times 10}\) ⇒ 960000/600 = 1600