Question

Karuna has an option to invest in the following three schemes. If she wants to invest Rs P, then which scheme will be most beneficial for her?

Scheme that comes with lower interest rates and terms;

I. 28% p.a. interest, compounded every quarter, for one year.

II. 28% p.a. interest, compounded every half year, for one year.

III. 28% p.a. interest, for one year, compounded every year.

1. I
2. III
3. II
4. All plans are equally beneficial

Answer 1

Correct Answer - Option 1 : I

Given:

I. 28% p.a. interest, compounded every quarter, for one year.

II. 28% p.a. interest, compounded every half year, for one year.

III. 28% p.a. interest, for one year, compounded every year.

Concept used:

Net effective rate = A + B + (AB)/100

where, 

A and B is Rate percent

Calculations:

Scheme I. 

28% p.a. interest, compounded every quarter, for one year.

Rate = 28/4 = 7%

Time = 4 × 1 = 4 years

Effective rate for 2 years = 7 + 7 + {(7 × 7)/100} = 14.49%

Effective rate for 3 years = 14.49 + 7 + {(14.49 × 7)/100} = 22.5043%

which is equivalent to 22.5%

Effective rate for 4 years = 22.5 + 7 + {(22.5 × 7)/100} = 31.075%

Scheme II. 

28% p.a. interest, compounded every half year, for one year.

Rate = 28/2 = 14%

Time = 2 × 1 = 2 years

Effective rate for 2 years = 14 + 14 + (14 × 14)/100 = 29.96%

Scheme III.

28% p.a. interest, for one year, compounded every year.

The overall rate of interest for one year is 28%

Clearly, we can see that Scheme I is more beneficial because it has a higher interest rate.

Thus, Scheme I is more beneficial.