Question

Sum of rupees 16000 rupees 1640 as interest in 2 years when compounded annually find the rate of interest

Answer 1

it is given that sum of 16000 Rs , 1640 Rs as interest in 2 years when compounded annually.

we have to find rate of interest,

using formula, C.I = P(1 + r/100)ⁿ - P

here, P = 16000 , n = 2 , C.I = 1640

1640 = 16000[(1 + r/100)² - 1]

here we know, 1 >> r/100

using binomial expansion, (1 + a)ⁿ ≈ 1 + na

so, (1 + r/100)² ≈ 1 + 2r/100 = 1 + r/50

⇒1640 = 16000[1 + r/50 - 1]

⇒164/1600 = r/50

⇒r = 164 × 50/1600 = 5.125 %

but we take approximation, so r is slightly less than 5.125 % i.e., 5%

so, the rate of interest must be 5 % per annum.

verification : C.I = 16000[(1 + 5/100)² - 1]

= 16000[441/400 - 1]

= 16000 × 41/400

= 1640 Rs

hence, rate of interest 5% per annum is correct.

Answer 2

Answer:

5%

Step-by-step explanation:

by using the A=P(1+1/100)^n