Ronak deposited ₹8000 at 10 % per annum for 2 years, comounded annually. What is the compound interest received by Ronak? How much more money will Ronak have in his account at the end of 2 years if it is compounded half-yearly
Answers
Answer:
1. Rs.1680
2. Rs.44.05
Step-by-step explanation:
P = principal or initial amount in Rupees = 8000
R = rate of interest per cent per year = 10
T = time period in years = 2
A = final amount at the end of time period T
Case 1: Annual compounding
A = P(1 + R/100)^T
A = 8000*(1 + 10/100)^2
= 8000*(1.1)^2
= 8000*1.21
= 9680
CI = Compound interest earned = A - P
CI = 9680 - 8000
= 1680
Compound interest earned in annual compounding = Rs.1680 ...(i)
Case 2: Half-yearly compounding
m = compounding interval = 2 [No. of intervals per year]
A = P[1 + (R/m)*100]^Tm
Now, R/m = 10/2 = 5; Tm = 2*2 = 4
=> A = 8000*(1 + 5/100)^4
= 8000*(1.05)^4
= 8000*(1.21550625)
= 9724.05
CI = A - P
= 9724.05 - 8000
= 1724.05
Compound interest earned in half-yearly compounding = Rs.1724.05 ...(ii)
From (i) and (ii), we have:
Excess amount earned from half-yearly compounding
= 1724.05 - 1680
= 44.05
Excess amount earned from half-yearly compounding is Rs.44.05
Answer:
CI received by Ronak (annual compounding) = Rs.1680
Excess amount on half-yearly compounding = Rs.44.05
Step-by-step explanation:
Ronak deposited 8000 at 10% per annum for 2 years, compounded annually. What is the compound
interest received by Ronak? How much more money will Ronak have in his account at the end of 2 years
if it is compounded half-yearly?
