Question

Aneesh took a loan of 25000 at 8% per annum interest being compounded half yearly .what amount will he pay
After 1 year
After 3/2 year

Answer 1

Principal Amount P = 25000 Rs.

Rate of Interest = 10% per annum

Since interest is compounded half yearly

Therefore, rate of interest for half year r =

10/2 = 5%

18 months = 3 half year

Therefore, period n = 3

Now, using the compound interest formula

A

= P(1+ 100)"

For the first 6 months (1 period), Amit

needs to pay

= 25000(1 + 160"

25000 x (1.05)

26250 Rs.

He paid = 8000 Rs. =

Now Principal amount = 262508000 = 18250

Now in the next 6 months Amit has to pay

= 18250(1+ 10)'

= 18250 x 1.05

= 19162.5 Rs.

Amit again paid Rs. = 8000

Thus, the new principal amount = 1916258000 = 11162.5 Rs.

In the next 6 months Amit has to pay

= 1116251 + 10)'

=

11162.5 x 1.05

= 11720625 Rs.Therefore, at the end of 18 months, Amit has to pay Rs. = 11720625

Hope this answer is helpful.

Hope it was helpful

Answer 2

S O L U T I O N :

$\underline{\bf{Given\::}}$

• Principal, (P) = Rs.25000
• Rate, (R) = 8%
• Time, (n) = 1 year & 3/2 year

$\underline{\bf{Explanation\::}}$

Using formula of the compounded half-yearly;

$\boxed{\bf{Amount= Principal\bigg(1+\frac{R/2}{100} \bigg)^{2n}}}$

A/q

$\mapsto\tt{Amount = 25000\bigg( 1+ \dfrac{8}{2\times 100} \bigg)^{(2\times 1)}}$

$\mapsto\tt{Amount = 25000\bigg( 1+ \cancel{\dfrac{8}{200}} \bigg)^{2}}$

$\mapsto\tt{Amount = 25000\bigg( 1+ \dfrac{1}{25} \bigg)^{2}}$

$\mapsto\tt{Amount = 25000\bigg( \dfrac{25+1}{25} \bigg)^{2}}$

$\mapsto\tt{Amount = 25000\bigg( \dfrac{26}{25} \bigg)^{2}}$

$\mapsto\tt{Amount = \cancel{25000} \times \dfrac{26}{\cancel{25}} \times \dfrac{26}{\cancel{25}} }$

$\mapsto\tt{Amount = Rs.(40\times 26 \times 26)}$

$\mapsto\bf{Amount = Rs.27040}$

Thus,

The amount he pay will be Rs.27040 .

Again,

$\mapsto\tt{Amount = 25000\bigg( 1+ \dfrac{8}{2\times 100} \bigg)^{(\cancel{2} \times 3/\cancel{2} )}}$

$\mapsto\tt{Amount = 25000\bigg( 1+ \dfrac{8}{2\times 100} \bigg)^{3}}$

$\mapsto\tt{Amount = 25000\bigg( 1+ \cancel{\dfrac{8}{200}} \bigg)^{3}}$

$\mapsto\tt{Amount = 25000\bigg( 1+ \dfrac{1}{25} \bigg)^{3}}$

$\mapsto\tt{Amount = 25000\bigg( \dfrac{25+1}{25} \bigg)^{3}}$

$\mapsto\tt{Amount = 25000\bigg( \dfrac{26}{25} \bigg)^{3}}$

$\mapsto\tt{Amount = \cancel{25000} \times \dfrac{26}{\cancel{25}}\times \dfrac{26}{\cancel{25}} \times \dfrac{26}{\cancel{25}}}$

$\mapsto\tt{Amount = Rs.(1.6 \times 26 \times 26 \times 26)}$

$\mapsto\bf{Amount = Rs.28121.6}$

Thus,

The amount will he pay Rs.28121.6 .