Ram borrowed a sum of Rs. 50,000 at 10% p.a. for 2 years compound interest compounded annually. On the same day, he lent this money to Hari at the same rate for same time of compound interest half yearly and on the same day Hari lent this money to Jiban at the same rate for the same time of compound interest quarterly.
a) Write the formula for finding quarterly compound interest.
How much amount did Hari return to Ram?
Who got more interest between Ram and Hari? Calculate and give a reason.
Answer (2)
Ram borrowed Rs. 50,000 at a 10% interest rate for 2 years, and after compounding half-yearly, he received Rs. 60,775.31 from Hari. Hari, compounding quarterly with the same principal and interest rate, received Rs. 60,920.10 from Jiban. Therefore, Hari earned more interest than Ram because of the more frequent compounding periods.
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Given:
Principal (P) = Rs. 50,000
Rate (R) = 10 percent per annum
Time (T) = 2 years
a) Formula for Quarterly Compound Interest:
For quarterly compounding:
Amount (A) = P × (1 + R/(4×100))^(4×T)
Where:
P = Principal
R = Rate of interest per annum
T = Time in years
b) How much amount did Hari return to Ram?
Ram lent money to Hari at the same rate, but compounded half-yearly.
For half-yearly compounding:
Number of half-years = 2 × 2 = 4
Rate per half-year = 10 percent / 2 = 5 percent
Amount Hari returns to Ram:
A = 50,000 × (1 + 0.05)^4
A = 50,000 × (1.21550625)
A = Rs. 60,775.31
c) Who got more interest between Ram and Hari?
Now, Hari lent the money to Jiban at the same rate, but compounded quarterly.
For quarterly compounding:
Number of quarters = 4 × 2 = 8
Rate per quarter = 10 percent / 4 = 2.5 percent
Amount Jiban returns to Hari:
A = 50,000 × (1 + 0.025)^8
A = 50,000 × (1.218402)
A = Rs. 60,920.10
Interest received by Ram:
= Rs. 60,775.31 - Rs. 50,000
= Rs. 10,775.31
Interest received by Hari:
= Rs. 60,920.10 - Rs. 50,000
= Rs. 10,920.10
Conclusion:
Hari got more interest than Ram because the frequency of compounding was higher (quarterly vs. half-yearly), leading to a greater amount due to more frequent addition of interest.
