Question

Find the compound interest on ₹ 31,250 at 5% pa for 2 1/2 years compounded annually.

Answer 1

Given:

Present value =₹ 31250

Interest rate =8% per annum

Time =1

2

1

year =3/2 year and compounded half-yearly

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=31250(1+(8/2)/100)

3

⇒A=31250(1+4/100)

3

⇒A=31250(1+1/25)

3

⇒A=31250(26/25)

3

⇒A=31250×17576/15625

⇒A=₹ 35152

∴ Compound interest =A–P

=35452–31250=₹ 3902

Answer 2

$₹ \: 4064.45$

Step-by-step explanation:

$Given, \: P=₹ \: 31250, \: \: r = 5 \% \: \: \: and \: \: \: \: n = 2 \frac{1}{2} \: year \\ we \: \: know \: \: \boxed{C.I =P(1 + \frac{r}{100} )^{n} - P} \\ Now, \: \: C.I = 31250(1 + \frac{5}{100} ) ^{2 \frac{1}{2} } - 31250\\ = 31250(1 + \frac{1}{20} )^{2 \frac{1}{2} } - 31250 \\ = 31250(1 + \frac{1}{20} )^{2} (1 + \frac{1}{20} )^{ \frac{1}{2} } - 31250 \\ = 31250(\frac{21}{20} )^{2} (1 + \frac{1}{2} \times \frac{1}{20} ) -31250 \\ = 31250(\frac{21}{20} )^{2} (1 + \frac{1}{40} ) - 31250\\ = 31250(\frac{21}{20} )^{2} (\frac{41}{40} ) - 31250\\ = 31250 \times \frac{441}{400} \times (\frac{41}{40} ) -31250 \\ = 35314.45 - 31250 \\ =₹ \: 4064.45$