Question

SIMPLE INTEREST AND COMPOUND INTEREST

Q.1 The simple interest and compound interest on a certain sum for 2 years are Rs. 800 and Rs.880 respectively. The rates of interests (in % p.a.) on both the sums is the same . If the interest on the sum lent at compound interest is compounded annually, find the rate of interest (in % p.a.).

Answer 1

Let the principal amount be x and the rate of interest be r
Now, Simple Interest on this amount for 2 years = PRT/100 = (x * r * 2)/100 = 2rx/100
Let r/100 be k.
Thus simple interest = 2xk = 800
⇒ 2xk = 800 --------------------------(1)
Now , Compound Interest on same amount for 2 years = P(1+(R/100))² -P = x(1 + (r/100))²- x = x(1 + k)² - x
= x(1 + k² + 2k ) - x = x + xk² + 2kx - x = x(k² + 2k) = 880
⇒ x(k² + 2k) = 880 -------------------------------(2)

Now dividing eq (1) by eq(2) we get
⇒ 2xk / x(k²+ 2k) = 800/880
⇒ 2k/ (k²+ 2k) = 10/11
⇒ 22k = 10( k²+ 2k)
⇒ 10k² + 20 k -22k =0
⇒ 10 k² - 2k = 0
⇒ 2k(5k - 1) = 0
⇒ k = 0 or 5k-1 = 0
⇒ k = 0 or k = 1/5
Now since k cannot be 0, thus k = 1/5
Thus , r/100 = 1/5
r = 100/5 = 20% pa