Question

A and B borrowed the same amount for the same period. A borrowed on simple interest at the rate of 8% yearly. B borrowed on compound interest of 5% half yearly. At the end of one year the ratio of B's interest to that of A's interest is:
1. 40 : 41
2. 32 : 41
3. 41 : 32
4. 4 : 3

Answer 1

Correct Answer - Option 3 : 41 : 32

Given:

Rate of interest of A = 8%

Rate of interest of B = 5%

Concept used:

For half year interest in CI = Interest rate/2

Successive increase concept = a + a + a²/100

a = rate %

Calculation:

5% half-yearly = 5 + 5 + (5 × 5)/100

⇒ 10 + 1/4

⇒ 41/4

So ratio of interest = 

41/4 : 8

⇒ 41 : 32

∴ ​At the end of one year the ratio of B's interest to that of A's interest is 41 : 32