Question

You are helping out your society to take a loan. They needed a sum of Rs

10,00,000. The maximum time period should be 3 years at rate of 10%p.a. You

should give them options of taking the loan with

I) Simple interest (rate calculated per annum)

II) Compound interest (rate calculated per annum)

III) Compound interest (rate calculated half yearly)

IV) show them the difference between simple interest and compound interest

V) Show them the difference between compound interest calculated yearly and

half yearly.​

Answer 1

Given:

Principle amount = P =  1000000

Time = T = 3 years

Rate = R =10% =0.1

To find:

1) Simple interest (per annum)

2) Compound interest (per annum)

3) Compound interest (half-yearly)

4) Difference between simple interest (per annum) and compound interest (per annum)

5) Difference between compound interest calculated per annum  and half-yearly.​

Step-by-step explanation:

1)

       Simple interest  = $\displaystyle \frac{P \times R \times T}{100}$

       S = $\displaystyle \frac{1000000 \times 0.1 \times 3}{100}$

      S = 3000

2)

Compound interest = $P \times (1+r)^T - P$

    A= 1000000  ($\times (1 + 0.1)^3$ - 1000000

   A = 331000

3)

Here T = 0.5 * 3 = 1.5

Compound interest = $P \times (1+r)^T -P$

    A= 1000000 $\times (1 + 0.1) ^ {1.5}$ - 1000000

   A = 153,689.73

4)

The difference between simple interest (per annum) and compound interest (per annum):

    D = 331000 -3000

   D = 328,000

5)

Difference between compound interest calculated per annum  and half-yearly.​

    D =  331000 - 153,689.73

   D = 177,310.27