A certain sum is interested at compound. The interest accrued in the first two years is rs. 544 and that in the first three years is rs. 868. Find the rate per cent.
Answers
Answer:
Rate of compound interest is 12.5.
Step-by-step explanation:
Let us define
P = principle, r = rate of compound interest, n = number of years.
I = Interest.
Compound interest is calculated from following equation
I = P((1 + r/100)^n – 1)
Given that interest for first 2 years is 544.
544 = P((1 + r/100)^2 – 1) -------------------------------- 1st Equation
Interest for first 3 years is 868
868 = P((1 + r/100)^3 – 1) ----------------------------------2nd Equaiton.
Let us define x = (1 + r/100)
Replacing X in above 2 equations and second equation divided by first equation gives us
868/544 = (x^3 – 1)/(x^2 – 1) = (x^2 + x + 1) (x – 1) / ((x + 1)(x -1))
= (x^2 + x + 1)/(x + 1)
(X^2+x+1) / (x + 1) = 217/136
136x^2 – 81x -81 = 0
X = 81 + √(81*81 + 4*136*81) / (2* 136) or 81 - √(81*81 + 4*136*81) / (2* 136)
X = 81 + √(50625)/2*136 or 81- √(50625)/2 * 136
X = (81 + 225)/2*136 or (81 – 225)/2*136
X = 9/8 (Ignoring the negative value)
(1 + r/100) = 9/8
R = 12.5
Hence rate of compound interest is 12.5.