Question

Vikram borrowed 20000 from a bank at 10% per annum simple interest. he lent it to his friend Venkat @ same rate but compared annually. Find his gain after two and a half years​

Answer 1

Answer:

Step-by-step explanation:

Principle amount(P) = 20000;

Rate of interest(R) = 10%;

Time(T) = 2.5 Years

Simple interest = PRT/100;

= 20000*10*2.5/100 = 5000;

Compound Interest = P{1 + R/100}^T;

Here rate of interest count as half yearly;

So R = R/2 and T = 5;

= 20000[1 + 10/2*100]^5;

= 20000[1.05]^5;

= 20000*1.27 = 25525.6

Gain =  Compound Interest - Simple Interest;

Gain = 25525.6-5000 = 20525.6

Answer 2

Answer:

Rs 380

Rs 410

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

$=20000 ( 1 + \frac{10}{100})^{2.5} - 20000\\\\= 20000 ( 1.1)^{2.5} - 20000\\\\= 20000(1.269) - 20000\\\\= 20000(0.269)\\\\= 5380$

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