Question

On what sum of money invested, if the difference between the compound interest and simple interest for 2 years at 9% per annum is $12960

Answer 1

Given info : difference between the compound interest and simple interest for 2 years at 9 % per annum is $ 12960.

solution : let P is principal amount , r = rate of interest = 9 % per annum and time = 2 years

so, compound interest , CI. = P[(1 + 9/100)² - 1]

= P[1 + (9/100)² + 2(9/100) - 1 ]

= P[9/100(9/100 + 2) ]

= 9/100 × (209/100) P

= 9 × 209P/100²

= 1881P/100²

simple interest , SI = Prt/100

= P × 9 × 2/100

= 18P/100

= 1800P/100²

given, CI - SI = $ 12960

⇒1881P/100² - 1800P/100² = 12960

⇒81P/100² = 12960

⇒P = 12960/81 × 100²

⇒P = 160 × 10000 = $ 16,00,000

Therefore the principal amount will be $ 16,00,000