Question

Vikram borrow 20000 from a bank at 10% per annum simple interest in lent it to his friend when comes at the same rate but compounded annually find his gain after 2 half years

Answer 1

The amount that accrued from the money that Vikram borrowed from the bank:

Simple interest formula:

A = P( 1 + rt)

A = amount accrued

P = Principle, original amount

r = % rate, in decimal

t = time in years.

Therefore the amount (A) that Vikram had to pay back to the bank after to half years ( which is 1 year) was:

A = 20000 ( 1 + 0.1×1)

A = 20000 × 1.1

A = $22000

Interest he has to pay;  22000 - 20000 = $2000

We can calculate the amount that Vikram will get after lending to his friend at compound interest at the same rate:

Compound interest formula:

A = P ( 1 + r/n)^nt

A  = amount accrued

P = principle amount, the original amount

r = % rate in decimal

n = number of compoundings in a year

t = number of years

Note:

-we will calculate compoundings of both semiannual and annul - since that was not clear in your question.

-Two half years is 1 year, so t  = 1


Annual compunding, n = 1


A = P ( 1 + r/n)^nt


A = 20000 ( 1 + 0.1/1)^1×1

A = 20000 × 1.1^1

A = 20000 × 1.1 = $22000

- Interest his friend will give him; 22000 -20000 = $2000

Semiannual compouding, n = 2


A = P ( 1 + r/n)^nt

A  = 20000 ( 1 + 0.1/2)^2×1

A = 20000 × 1.05^2

A = 20000 × 1.1025  = $22050

- interest his friend will give him if compounded twice a year; 22050 - 20000 = $2050

⇒Therefore if he lent to his friend compounding annually the profit would be:

2000 - 2000 = 0 , no profit

⇒ Therefore if he lent to his friend compounding semiannually, twice a year, the profit would be; 2050 - 2000 = $50

Answer 2

Therefore ,

Vikram gain the amount = ( 4 ) - ( 1 )

= 5410 - 5000

= Rs 410
I hope this helps you.

: )