Question

What is the rate of interest if there is a difference of 121.50 between the simple interest and compound interest on principal of 15000 for 2 years

Answer 1

rate of interest is 9% per annum.

Given, initial amount, P = 15,000

time , n = 2 yrs

C.I - S.I = 121.50

let the rate of interest per annum is r.

here S.I = P × r × n/100

= 15000 × r × 2/100

= 150 × r × 2

= 300r

C.I = P(1 + r/100)ⁿ - P

= 15000(1 + r/100)² - 15000

= 15000[1 + r²/100² + 2r/100 - 1 ]

= 15000[r²/100² + 2r/100]

now, 15000[r²/100² + 2r/100] - 300r = 121.5

⇒15000r²/10000 + 300r - 300r = 121.5

⇒15r²/10 = 121.5

⇒3r² = 243

⇒r² = 81

⇒r = 9

hence rate of interest is 9% per annum.

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