Question

Nirmal took a loan of Rs 60000 from a bank. The rate of interest is 10% per annum. Find the difference in amounts she would be paying after 1½ years if the interest is

a) Compounded half yearly
b) Compounded annually​

Answer 1

$\: \bf \red { ☆_!! Question !_! ☆}$

Nirmal took a loan of Rs 60000 from a bank. The rate of interest is 10% per annum. Find the difference in amounts she would be paying after 1½ years if the interest is

a) Compounded half yearly

b) Compounded annually

$\bf\green{ ☆_!! Answer !_! ☆} \: (a \: part)$

a) Compounded half yearly -

$\begin{gathered}\bf\gray{Given}\begin{cases}\sf\red{Principal\: ( rs \: 60000)}\\\sf\green{Rate\:(10\%p.a )}\\\sf\pink{time(n)\:(1 \frac{1}{2} \: years )} \end{cases}\end{gathered}$

Rate = 10 % p.a

→ 10/2 % per half year

→ 5 % per half year

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Time (n) = 1½ years

→ 3/2 years

→ 3/2 × 2 half years

→ 3 half years

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Let's solve it .................. ✍️

$\sf Amount = principal (1 + \dfrac{rate}{100} )^{n}$

$\sf Amount =rs [ 60000(1 + \dfrac{5}{100} )^{3}$ ]

$\sf Amount = rs [ 60000 ( \frac{21}{20} )^{3}$ ]

$\sf Amount = rs [ 60000 \times \dfrac{21}{20} \times \dfrac{21}{20} \times \dfrac{21}{20} ]$

$\sf Amount = rs 69457.50$

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$\bf\green{ ☆_!! Answer !_! ☆} \: (b \: part)$

b) Compounded annually -

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$\begin{gathered}\bf\gray{Given}\begin{cases}\sf\red{Principal\: ( rs \: 60000)}\\\sf\green{Rate\:(10\%p.a )}\\\sf\pink{time\:(1 \frac{1}{2} \: years )} \end{cases}\end{gathered}$

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Let's solve it .................. ✍️

$\sf Amount = principal \: (1 + \dfrac{rate}{100} )(1 + \dfrac{ \dfrac{1}{2} \times rate }{100} )$

$\sf Amount = rs[60000 \: (1 + \dfrac{10}{100} )(1 + \dfrac{ \dfrac{1}{2} \times 10 }{100} )]$

$\sf Amount = rs[60000 \: ( \dfrac{11}{10} )(\dfrac{ 21 }{20} )]$

$\sf Amount = rs \: 69300$

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★Difference in amounts =

→ rs (69457.50 - 69300 )

→ rs 157.50

Hence, Nirmal would have to pay rs 157.50 more if the compound interest is compounded half yearly