Question

Vikram borrowed 20000 from a bank at 10% per annum simple interest he lent it to his friend Venkat at the same rate but compounded annually find his gain after 2 and half year please explain​

Answer 1

Answer:

Step-by-step explanation:

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,

⇒20000(1+10/100)∧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,

Hope it helps.