Question

If the rate of Compound interest is 12 % per year and compound interest is calculated every 3 months, then what is the total amount after 9 months when the deposited amount is one lakh ?
[A] Rs.1,09,000.00
[B] Rs.1,09,060.00
[C] Rs.1,09,060.30
[D] Rs.1,09,272.70

Explain?

Answer 1

Question :------ we have to find amount ...

Given :-----

• Rate = 12% per year
• Time = 9 months
• interest is compounded Quarterly .
• Principal = 1 lakh

we know that, when interest is compounded Quarterly ,

Time will be 4 times , and rate is divided by 4 ..

so,

our Time is = 9*4 = 36 months = 3 years.

out Rate is = 12/4 = 3% per yearly now .

Now we know that :------

$\huge\red{\boxed{\sf A\:=\:P( 1 + \frac{r}{100})^{t}}}$

Putting values now we get,

$A = 100000(1 + \frac{3}{100} )^{3} \\ \\ A = 100000 ( \frac{103}{100} )^{3} \\ \\ A = \frac{ \cancel{10000}0 \times 103 \times 103}{ \cancel{100 \times 100}} \\ \\ A = 106090$

So our Amount after 9 months will be 1,06,090 (None of these options are correct )

( Hope it helps you )

Answer 2

$\huge\mathcal\purple{Solution}$

given that :-

$\sf\implies$ Principal = 100000

$\sf\implies$Rate = 12%

Rate is for quarterly = 12/4 = 3

$\sf\implies$Time = 9

Time is for quaterly = 9 × 4 = 36 = 3years

Then according to questions :-

$\huge\boxed{A = P({1 + \frac{r}{100}})^{t}}$

putting the values

$A = 100000{(1 + \frac{3}{100})}^{3}\\ \\ A = 100000{(\frac{103}{100})}^{3} \\ \\ A = \frac {100000 × 103 × 103 × 103 }{100 × 100 × 100} \\ \\ A = \frac{103 × 103 × 103 } {10} \\ \\ A = \frac{1,092,727}{10} \\ \\ A = 1,092,72.7$

Options D is correct Rs 1,092,72.70