Question

Thomas took out a loan of 20000 rupees from a bank which charges 10% interest , compounded annually . after two years , he paid back 10000 rupees . to settle the loan , how much should he pay at the end of three years ?

Answer 1

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

Given that,

Thomas took out a loan of Rs 20000 from a bank which charges 10% interest , compounded annually . After two years , he paid back Rs 10000 to settle the loan.

Let we first find the outstanding amount at the end of 2 years.

So, given that,

Principal amount = Rs 20000

Rate of interest, r = 10 % per annum compounded annually

Time, n = 2 years.

We know that,

Amount on a certain sum of money of Rs 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

$\rm :\longmapsto\:Amount = 20000 {\bigg[1 + \dfrac{10}{100} \bigg]}^{2}$

$\rm :\longmapsto\:Amount = 20000 {\bigg[1 + \dfrac{1}{10} \bigg]}^{2}$

$\rm :\longmapsto\:Amount = 20000 {\bigg[ \dfrac{10 + 1}{10} \bigg]}^{2}$

$\rm :\longmapsto\:Amount = 20000 {\bigg[ \dfrac{11}{10} \bigg]}^{2}$

$\rm :\longmapsto\:Amount = 20000 \times \dfrac{11}{10} \times \dfrac{11}{10}$

$\rm \implies\:\boxed{ \tt{ \: Amount \: = \: Rs \: 24200 \: }}$

As, Thomas pay Rs 10000 at the second year.

So, outstanding amount = 24200 - 10000 = Rs 14200

Now, for third year

Principal amount = Rs 14200

Rate of interest, r = 10 % per annum compounded annually.

Time, n = 1 year

So,

$\rm :\longmapsto\:Amount = 14200\bigg[1 + \dfrac{10}{100} \bigg]$

$\rm :\longmapsto\:Amount = 14200\bigg[1 + \dfrac{1}{10} \bigg]$

$\rm :\longmapsto\:Amount = 14200\bigg[\dfrac{10 + 1}{10} \bigg]$

$\rm :\longmapsto\:Amount = 14200\bigg[\dfrac{11}{10} \bigg]$

$\rm \implies\:\boxed{ \tt{ \: Amount \: = \: Rs \: 15620 \: }}$

So,

• Thomas has to pay Rs15, 620 at the end of third year.

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Additional Information :-

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

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