Let rate = R % per annum
P = Rs.4000
A = Rs.4410
Time = 2 years
Now,
Amount (A) = P (1 + R/100)n [Where, A = Amount with compound interest
P = Present value
R = Annual interest rate
n = Time in years]
∴ A = P (1 + R/100)2
⇒ 4410 = 4000 (1 + R/100)2
⇒ (1 + R/100)2 = 4410/4000
⇒ (1 + R/100)2 = 441/400
⇒ (1 + R/100) = √(441/400)
⇒ R/100 = (21/20) - 1
⇒ R/100 = (21 – 20)/20
⇒ R/100 = 1/20
⇒ R = 100/20
⇒ R = 5
∴ Rate = 5% per annuam.
Home
At what rate percent per annum will a sum of Rs. 4000 yield compound interest of Rs. 410 in 2 years?
Open in App
Solution
Principal (P) = Rs. 4000
C.I = Rs. 410
∴ Amount (A) = Rs.
4000 + 410 = Rs. 4410
Let rate =R% p.a.
Period (n) = 2 years.
∴ Amount
=P(1+R100)n
⇒AP=(1+R100)2
⇒Rs.44104000=(1+R100)n
⇒4414000=[1+R100]2
⇒(2120)2=(1+R100)2
Comparing, we get
1+R100=2120=1+120
∴R100=120⇒R=10020=5
∴ Rate =5% p.a
Suggest Corrections
37
Same exercise questions
Q.
A sum amounts to Rs. 756.25 at 10% per annum in 2 years, compounded annually. Find the sum.
Q.
What sum will amount to Rs. 4913 in 18 months, if the rate of interest is 1212% per annum, compounded half-yearly.
Q.
Find the principal of the interest compounded annually at the rate of 10% for two years is Rs. 210.
Q.
The difference between the compound interest and simple interest on a certain sum at 15% per annum for 3 years isRs. 283.50. Find the sum.
Q.
On what sum will the compound interest at 5% p.a. annum for 2 years compounded annually be Rs. 164?
View More