Question

1. If rs.1600 lent at a Cl of 5%p.a, then compounded half yearly for 1 year. What will be the amount to?​

Answer 1

$\sf{\star}$ Given:-

• Principal = Rs.1600
• Rate = 5%
• Time = 1 year [compounded half-yearly]

$\sf{\star}$To Find:-

Amount after 1 year

$\sf{\star}$ Solution:-

We know,

$\sf{A = P\bigg(1+\dfrac{r}{200}\bigg)^{2n}}$

= $\sf{A = 1600\bigg(1+\dfrac{5}{100}\bigg)^{2\times1}}$

= $\sf{A = 1600\bigg(1+\dfrac{\not{5}}{\not{100}}\bigg)^2}$

= $\sf{A = 1600\bigg(1+\dfrac{1}{20}\bigg)^2}$

= $\sf{A = 1600\bigg(\dfrac{20+1}{20}\bigg)^2}$

= $\sf{A = 1600\bigg(\dfrac{21}{20}\bigg)\bigg(\dfrac{21}{20}\bigg)}$

= $\sf{A = 16\times21\times21}$

= $\sf{A = 7056}$

Therefore The amount after 1 years (compounded half-yearly) will be Rs.7056.

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$\sf{\star}$ Information:-

Use:-

$\sf{A = P\bigg(1+\dfrac{r}{100}\bigg)^t}$

When principal will be compounded annually.

Use:-

$\sf{A = P\bigg(1+\dfrac{r}{400}\bigg)^{4t}}$

When Principal will be compounded quarterly.

Use:-

CI = A - P

To find Compound Interest After finding the amount.

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$\sf{\star}$ Note:-

A = Amount

P = Principal

t = Time (Also denoted by n)

r = Rate

CI = Compound Interest

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