Question

find the amount and the compound interest on 50000 for two and half years at 12 percent compounded half yearly would this interest be more if it is compounded quarterly and by how much

Answer 1

Solution

Principal = ₹50,000

Time = 2 ½years = 5/2years

Rate = 12%p.a.

Calculation for the interest compounded half-yearly

Principal = ₹50,000

Time = 5/2years = 5×2/2 = 5years.

Rate = 12%p.a. = 12/2 = 6%p.a.

$\bf{A = P\bigg\{1+\dfrac{R}{100}\bigg\}^n}$

$\sf{ = 50000\bigg\{1+\dfrac{6}{100}\bigg\}^{5}}$

$\sf{ = 50000 \bigg \{ \dfrac{100 + 6}{100} \bigg \}^{5} }$

$\sf{ = 50000 \bigg \{\dfrac{53}{50} \bigg\}^{5} }$

$\sf{= \cancel{50000} \times\dfrac{418195493}{ \cancel{312500000}} }$

$\sf\therefore{Amount= \boxed{₹66,911.28}(approx)}$

$\bf{C.I.=A-P}$

$\sf{ = 66911.28-50000}$

$\sf\therefore{Compound \: Interest=\boxed{₹16,911.28}}$

$\rule{210pt}{1pt}$

Calculation for the interest compounded quarterly

Principal = ₹50,000

Time = 5/2 years = 5×4/2 = 10years

Rate = 12%p.a. = 12/4 = 3%p.a.

$\bf{A = P\bigg\{1+\dfrac{R}{100}\bigg\}^n}$

$\sf{ =50000\bigg \{1+\dfrac{3}{100} \bigg \}^{10} }$

$\sf{ = 50000 \bigg \{ \dfrac{100 + 3}{100} \bigg\}^{10} }$

$\sf{ = 50000 \times \bigg \{ \dfrac{103}{100} \bigg \}^{10} }$

$\sf{ = 50000 \times 1.3439}$

$\sf\therefore{Amount= \boxed{₹67,195}}$

$\bf{C.I.=A-P}$

$\sf{ = 67195 - 50000}$

$\sf\therefore{Compound\:Interest= \boxed{₹17,195}}$

Difference of Interests = ₹17,195 - ₹16,911.28

= ₹283.72.

Hence,

• Interest compounded quarterly will be more than the interest compounded half-yearly by ₹283.72.

${ \underline{\rule{210pt}{4pt}}}$

Answer 2

Answer:

23468op0

Step-by-step explanation:

• chuutiyap ke liye paise nhi hai to get the chance to win
• 500999
• 5000090 - 12 /0/
• 66911 your answer the question