Question

Mario took loan of ₹50000 from Bank at the rate of interest 8% per annum compounded manually.
Find intrest earned in first year. What will be the principle for second year?
Find compound interest for 3 years
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Answer 1

Answer:

Step-by-step explanation:

Compounded annualy should be there

use

A=P(1+r)^n

A=50000 (1.08) (For first year)

A=54000

I=54000-50000 which is earned by bank=4000

principal for second year is 54000

amt after three yrs

50000 (1.08)^3=62985.6

Interest=12985.6

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

• Mario took loan of ₹ 50000 from Bank at the rate of interest 8% per annum compounded anually.

It means

• Principal amount, p = ₹ 50000

• Rate of interest, r = 8 % per annum compounded annually.

We know,

Interest (I) received on a sum of money of ₹ p invested at the rate of r % per annum compounded annually for one year is given by

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: I \: = \: \dfrac{p \times r}{100} \: }}}$

So, on substituting the values, we get

$\rm :\longmapsto\:I \: = \: \dfrac{50000 \times 8}{100} = 4000$

So, Interest earned in the first year = ₹ 4000

Principal for second year = ₹ 50000 + ₹ 4000 = ₹ 54000

Now, We have

• Principal amount, p = ₹ 50000

• Rate of interest, r = 8 % per annum compounded annually.

• Time, n = 3 years

We know that

Amount on a certain sum of money of ₹ p invested at the rate of r % per annum compounded annually for n years is

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: Amount = p {\bigg[1 + \dfrac{r}{100} \bigg]}^{n} \: }}}$

So, on substituting the values, we get

$\rm :\longmapsto\:Amount = 50000 {\bigg[1 + \dfrac{8}{100} \bigg]}^{3}$

$\rm :\longmapsto\:Amount = 50000 {\bigg[1 + \dfrac{2}{25} \bigg]}^{3}$

$\rm :\longmapsto\:Amount = 50000 {\bigg[\dfrac{25 + 2}{25} \bigg]}^{3}$

$\rm :\longmapsto\:Amount = 50000 {\bigg[\dfrac{27}{25} \bigg]}^{3}$

$\rm :\longmapsto\:Amount = 50000 \times \dfrac{27}{25} \times \dfrac{27}{25} \times \dfrac{27}{25}$

$\bf\implies \:Amount = 62985.60$

Now, we know

Compound Interest = Amount - Principal

Thus,

Compound interest = 62985.60 - 50000 = ₹ 12985.60

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1. Amount on a certain sum of money of ₹ p invested at the rate of r % per annum compounded semi - annually for n years is

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: Amount = p {\bigg[1 + \dfrac{r}{200} \bigg]}^{2n} \: }}}$

2. Amount on a certain sum of money of ₹ p invested at the rate of r % per annum compounded quarterly for n years is

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: Amount = p {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n} \: }}}$

3. Amount on a certain sum of money of ₹ p invested at the rate of r % per annum compounded monthly for n years is

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: Amount = p {\bigg[1 + \dfrac{r}{1200} \bigg]}^{12n} \: }}}$