Question

If Rs 15000 is invested at 20% per annum for 1 year, if one time rate is compounded Quarterly and another time rate is compounded Semi annually, then what will be the difference between the interest earned in two cases?
1. Rs 85
2. Rs 83
3. Rs 82.6
4. Rs 90.3

Answer 1

Correct Answer - Option 3 : Rs 82.6

Given;

Principal = Rs 15000 , Rate = 20% per annum , Time = 1 year

Formula Used;

\({\rm{A}} = P{\left[ {1 + \frac{r}{{100}}} \right]^n}\)

C.I. = Amount - Principal

Concept Used:

If rate is compounded Quarterly, 

then Rate = 20/4 = 5% per quarter

Time period = 4

If Rate is compounded Semi annually then,

Effective Rate = 20/2 = 10% per half year

Time period = 2

Calculation:

Amount earned if interest is compounded Quarterly,

Amount = \({\rm{A}} = 15000{\left[ {1 + \frac{5}{{100}}} \right]^4}\)

⇒ A = [15000 × (21)⁴]/(20)⁴

⇒ A = (15 × 194481)/160

⇒ A = Rs 18232.6

C.I. = 18232.6 - 15000 = Rs 3232.6

Amount earned if rate is compounded Semi annually,

 \({\rm{A}} = 15000{\left[ {1 + \frac{{10}}{{100}}} \right]^2}\)

⇒ A = (15000 × 11 × 11)/(10 × 10)

⇒ A = Rs 18150

C.I. = 18150 - 15000 = Rs 3150

Difference between two cases = 3232.6 - 3150 = Rs 82.6

∴ The difference between the interest earned during two cases is Rs 82.6