Question

Calculate the amount and compound intrest on Rs 80,000 for 18 months at 10% per anum compounded halfyearly​

Answer 1

Answer :

To Find :-

⠀⠀⠀⠀⠀⠀⠀$\bigstar$ The Compound Interest.

⠀⠀⠀⠀⠀⠀⠀$\bigstar$ Amount.

Given :-

• Principal = Rs. 80,000

• Time = 18 months

• Rate of interest = 10 % p.a.

We know :-

⠀⠀⠀Amount for n years x months :-

⠀⠀⠀⠀⠀⠀⠀⠀⠀(Compounded Half-yearly)

$\underline{\boxed{\bf{A = P\bigg(1 + \dfrac{R}{200}\bigg)^{2n}\bigg(1 + \dfrac{R \times \dfrac{x}{12}}{100}\bigg)}}}$

Where :-

⠀⠀⠀⠀⠀⠀⠀⠀$\star$⠀A = Amount

⠀⠀⠀⠀⠀⠀⠀⠀$\star$⠀P = Principal

⠀⠀⠀⠀⠀⠀⠀⠀$\star$⠀R = Rate of interest

⠀⠀⠀⠀⠀⠀⠀⠀$\star$⠀n = no. of years.

⠀⠀⠀⠀⠀⠀⠀⠀$\star$⠀x = no. of months

⠀⠀⠀⠀ Compound Interest :-

$\underline{\boxed{\bf{CI = Amount - Principal}}}$

Solution :-

⠀⠀⠀⠀⠀⠀⠀Amount :-

To Find the amount using the formula , first let us convert the time in months and years from months.

We know ,

⠀⠀⠀⠀⠀⠀⠀1 year = 12 months.

So , in 18 months , we get :-

⠀⠀⠀⠀⠀⠀18 months = 1 years (18 - 12) months

⠀⠀⠀⠀⠀==> 18 months = 1 years 6 months

Hence, the time period is 1 year 12 months.

Now ,

By using the formula and substituting the values in it, we get :-

$:\implies \bf{A = P\bigg(1 + \dfrac{R}{200}\bigg)^{2n}\bigg(1 + \dfrac{R \times \dfrac{x}{12}}{100}\bigg)}$

$:\implies \bf{A = 80000 \times \bigg(1 + \dfrac{10}{200}\bigg)^{2 \times 1}\bigg(1 + \dfrac{10 \times \dfrac{6}{12}}{100}\bigg)}$

$:\implies \bf{A = 80000 \times \bigg(1 + \dfrac{10}{200}\bigg)^{2}\bigg(1 + \dfrac{10 \times \dfrac{1}{2}}{100}\bigg)}$

$:\implies \bf{A = 80000 \times \bigg(1 + \dfrac{10}{200}\bigg)^{2}\bigg(1 + \dfrac{5}{100}\bigg)}$

$:\implies \bf{A = 80000 \times \bigg(\dfrac{200 + 10}{200}\bigg)^{2}\bigg(\dfrac{100 + 5}{100}\bigg)}$

$:\implies \bf{A = 80000 \times \bigg(\dfrac{210}{200}\bigg)^{2}\bigg(\dfrac{105}{100}\bigg)}$

$:\implies \bf{A = 80000 \times \bigg(\dfrac{21}{20}\bigg)^{2}\bigg(\dfrac{21}{20}\bigg)}$

$:\implies \bf{A = 80000 \times \dfrac{21}{20} \times \dfrac{21}{20} \times \dfrac{21}{20}}$

$:\implies \bf{A = 80000 \times \dfrac{9291}{8000}}$

$:\implies \bf{A = 10 \times 9291}$

$:\implies \bf{A = 92910}$

$\therefore \purple{\bf{Amount = Rs. 92610}}$

Hence, the amount Gained is Rs. 92610.

⠀⠀⠀⠀⠀⠀⠀Compound interest :-

Given :-

• Principal = Rs. 80,000

• Amount = Rs. 92610

Using the formula and substituting the values in it, we get :-

$\boxed{\begin{minipage}{7 cm} Compound Interest :- \\ :\implies \bf{CI = A - P} \\ :\implies \bf{CI = 92610 - 80000} \\ :\implies \bf{CI = 12610} \\ \therefore \bf{Compound\:Interest = Rs. 12610} \end{minipage}}$

Hence, the compound interest is Rs. 12610.