Question

Indu lent out ₹18000 for 2 years at 20% per annum compounded annually. How much more could she earn, if the interest were compounded half- yearly

Answer 1

Amount →

If compound annually

$amount \: = p(1 + { \frac{r}{100}) }^{n}$

If compound half yearly

$amount \: = p( {1 + \frac{ \frac{r}{2} }{100}) }^{2n}$

Given that -

• Principal (p) = rs 18000
• Rate(r) = 20%
• Time (n) = 2 years

1st case (annually)→

$amount \: = 18000( {1 + \frac{20}{100} )}^{2}$

Amount = 18 ×12×120

Amount = rs 25920

2nd case ( half yearly) →

$amout \: = 18000( {1 + \frac{ \frac{20}{2} }{100} )}^{2 \times 2}$

Amount = 18×11×11×11×1.1

Amount = rs 26353.8

Extra earning = 2nd case - 1st case

Extra earning = 26253.8 - 25920

Extra earning = rs 433.8

hope it helps

__________________________❤

Answer 2

Step-by-step explanation:

compound annually

\begin{gathered}amount \: = p(1 + { \frac{r}{100}) }^{n} \\ \end{gathered}

amount=p(1+

100

r

)

n

If compound half yearly

\begin{gathered}amount \: = p( {1 + \frac{ \frac{r}{2} }{100}) }^{2n} \\ \end{gathered}

amount=p(1+

100

2

r

)

2n

Given that -

Principal (p) = rs 18000

Rate(r) = 20%

Time (n) = 2 years

1st case (annually)→

\begin{gathered}amount \: = 18000( {1 + \frac{20}{100} )}^{2} \\ \end{gathered}

amount=18000(1+

100

20

)

2

Amount = 18 ×12×120

Amount = rs 25920

2nd case ( half yearly) →

\begin{gathered}amout \: = 18000( {1 + \frac{ \frac{20}{2} }{100} )}^{2 \times 2} \\ \end{gathered}

amout=18000(1+

100

2

20

)

2×2

Amount = 18×11×11×11×1.1

Amount = rs 26353.8

Extra earning = 2nd case - 1st case

Extra earning = 26253.8 - 25920

Extra earning = rs 433.8

hope it helps

__________________________❤