Question

abhay borrowed rs 16000 at 7.5% per annum simple interest.on the same day . he lent it to gurmeet at the same rate but compounded anually. what does he gain at the end of 2 years?

Answer 1

See here the question is divided into two parts
1st - we will calculate the interest which he has to pay after two
S.I =P×R×T/100
= 16000×7.5×2/100
=2400.
and now we will calculate the interest which he will receive from Gurmeet.
A=P(1+i/m)^nm
=16000(1+0.075)^2
=18490
S.I from Gurmeet= A-P
=18490-16000
=2490.
So
after calculating the two values.
2490-2400=90
90 is the gain he earned after two years.

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Answer 2

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Present value = ₹ 16000

Interest rate = 7 ½ % per annum = 15/2 %

Time =2 years

Now find compound interest,

To find the amount we have the formula,

Amount (A) = P (1+(R/100))^n

Where P is present value, r is rate of interest, n is time in years.

Now substituting the values in above formula we get,

∴ A = 16000 (1 + (15/2)/100)²

⇒ A = 16000 (1+3/40)²

⇒ A =16000 (43/40)²

⇒ A = 16000 (1894/1600)

⇒ A = ₹ 18490

∴ Compound interest = A – P

= 18490 – 16000 = ₹ 2490

Now find the simple interest,

Simple interest (SI) = PTR/100

Where P is principle amount, T is time taken, R is rate per annum

SI = (16000 × (15/2) × 2) / 100

= 160 × 15

= ₹ 2400

Abhay gains at the end of 2 year= (CI – SI)

= 2490 – 2400

= ₹ 90

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