Question

A's captial exceeds B's capital by 20.5% invests his capital at 20% p.a for 3yr interest compounded annually.At what rate percentage p.a must A invest his capital at simple interest so that at the end of 3 yrs both get the same ammount?​

Answer 1

Question :- A's captial exceeds B's capital by 20.5%. B invests his capital at 20% p.a for 3years interest compounded annually. At what rate percentage p.a must A invest his capital at simple interest so that at the end of 3 yrs both get the same ammount ?

Solution :-

Let us assume that, B's capital is Rs.100 .

Than,

→ A's captial = exceeds B's capital by 20.5%.

→ A's captial = 20.5% exceeds than Rs.100

→ A's captial = (120.5 * 100)/100 = Rs.120.5 .

Now,

→ B's captial = Rs.100

→ Rate = 20% PA compounded annually.

→ Time = 3 years.

So,

→ Amount = (Capital) * [ 1 + (Rate/100)]^(Time)

→ Amount = 100 * [ 1 + (20/100) ]³

→ Amount = 100 * [ 1 + (1/5) ]³

→ Amount = 100 * (6/5)³

→ Amount = 100 * (216/125)

→ Amount = Rs.172.5

Now,

→ A's captial = Rs.120.5

→ Rate = Let R% annually.

→ Time = 3 years.

→ Amount = Principal + (Principal * Rate * Time/100)

→ Amount = 120.5 + (120.5 * R * 3/100)

→ Amount = Rs.(120.5 + 3.615R)

Now, we have given that, both received same amount .

Therefore,

→ 120.5 + 3.615R = 172.5

→ 3.615R = 172.5 - 120.5

→ 3.615R = 52

→ R ≈ 14.38%

Hence, A invest his capital at 14.38% simple interest so that at the end of 3 years both get the same amount.

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Answer 2

Answer:

14.5

Step-by-step explanation:

Let us assume that, B's capital is Rs.100 .

Then,

• A's capital exceeds B's capital by 20.5%.  

          • A's capital = (20.5/100)*100 + 100 = Rs.120.5 .

Now,  we know that

• B's capital = Rs.100

• Rate = 20% p.a. compounded annually.

• Time = 3 years.

So,

Amount = (Capital) * [ 1 + (Rate/100)]^(Time)

Amount = 100 * [ 1 + (20/100) ]³

Amount = 100 * [ 1 + (1/5) ]³

Amount = 100 * (6/5)³

Amount = 100 * (216/125)

Amount = Rs.172.8

Now,

A's capital = Rs.120.5  

Rate = Let R% annually.

Time = 3 years.

Amount = Capital + (Capital* Rate * Time/100)

Amount = 120.5 + (120.5 * R * 3/100)

Amount = Rs. (120.5 + 3.615R)

Now, we have given that, both get the same amount .

Therefore,

120.5 + 3.615R = 172.8

3.615R = 172.8 - 120.5

3.615R = 52 .3

R = 14.46 or 14.5 (roundoff)

Hence, A invest his capital at 14.5% simple interest so that at the end of 3 years both get the same amount.