Question

Abhay borrowed тВ╣16000 at 7.5% per annum simple interest on the same day he lent it to Gurmeet at the same rate but compounded annually what does he gains at the end of two 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.

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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