vikram borrowed rs 20000 from a bank at 10%p.a. simple interest. he lent it to his friend venkat at the same rate but compounded annually. find his gain after 2 and 1/2 years.
Answers
Answer:
Simple interest = P * R * n/100
P = Principle = Rs 20000
R = 10% per annum
n = 2.5 Years
Simple interest for 2.5 Years = 20000 * 10 * (2.5)/100 = Rs 5000
Compound interest = P ( 1 + r/100)ⁿ - P
\begin{gathered}=20000 ( 1 + \frac{10}{100})^{2.5} - 20000\\\\= 20000 ( 1.1)^{2.5} - 20000\\\\= 20000(1.269) - 20000\\\\= 20000(0.269)\\\\= 5380\end{gathered}
=20000(1+
100
10
)
2.5
−20000
=20000(1.1)
2.5
−20000
=20000(1.269)−20000
=20000(0.269)
=5380
Gain = Compound interest - Simple Interest
=> Gain = 5380 - 5000
=> Gain = Rs 380
This is based on formula of compound interest
as this formula start compounding for a smaller period than compounding period but in actual compounding is done at per mentioned period only
But if we do it other way
Simple interest & Compound interest for 1st year = Equal
= 20000 * 10 * 1/100 = Rs 2000
in Second year
Simple interest = Rs 2000 again
now compound interest will be calculated on interest gained also
but compound interest = (20000 + 2000) * 10 * 1/100 = Rs 2200
Additional Compound interest = Rs 200
in 3rd year for 6 months = (0.5 Years)
Simple interest = 20000 * 10 * 0.5/1000 = 1000
Compound interest = (20000 + 2000 + 2200) * 10 * 0.5/100
= 1210
Extra interest in 6 months for 3 rd year = 1210 - 1000 = Rs 210
Total extra interest = Rs 200 + 210 = 410
Gain = Rs 410