# 1. Calculate the amount and compound interest on 18,000 for 1(½) years at 10% perannum compounded half yearly.​

1. Calculate the amount and compound interest on 18,000 for 1(½) years at 10% per
annum compounded half yearly.​

1. ## Given :-

• Principal = ₹18000
• Time = 1½ years → 3/2 years
• Rate = 10%
• Compounded half-yearly

## Aim :-

• To find the amount and compound interest

## Formula to use :-

$$\longrightarrow \sf{amount = principal \bigg(1 + \dfrac{rate}{200} \bigg) ^{2 \times time}}$$

$$\longrightarrow \sf{compound \: interest = (amount) – (principal)}$$

Substituting the values,

## Amount :-

$$\implies \sf{amount = 18000 \bigg( 1 + \dfrac{10}{200} \bigg)^{2 \times \frac{3}{2} } }$$

$$\implies \sf{amount = 18000 \bigg(1 + \dfrac{1 \not0}{20 \not0} \bigg)^{ \not2 \times \frac{3}{ \not2} } }$$

$$\implies \sf{amount = 18000 \bigg( \dfrac{20 + 1}{20} \bigg)^{3} }$$

$$\implies \sf{amount = 18000 \bigg( \dfrac{21}{20} \bigg)^{3} }$$

$$\implies \sf{amount = 18000 \times \dfrac{21}{20} \times \dfrac{21}{20} \times \dfrac{21}{20} }$$

$$\implies \sf{amount = 18 \not0 \not0 \not0 \times \dfrac{21}{2 \not0} \times \dfrac{21}{2 \not0} \times \dfrac{21}{2 \not0} }$$

Cancelling 18 and 2, as they are divisible,

$$\implies \sf{amount = 9 \times 21 \times \dfrac{21}{2} \times \dfrac{21}{2} }$$

$$\implies \sf{ amount = \dfrac{83349}{4}}$$

$$\implies \sf{amount = 20837.25}$$

## Compound interest :-

Substituting the values,

$$\implies \sf{20837.25 – 18000}$$

$$\implies \sf{2837.25}$$

## Some more formulas :-

• When interest is compounded yearly :-

$$\longrightarrow \sf{amount = principal \bigg(1 + \dfrac{rate}{100} \bigg) ^{time} }$$

• When interest is compounded quarterly :-

$$\longrightarrow \sf{amount = principal \bigg(1 + \dfrac{rate}{400} \bigg)^{4 \times time} }$$

• Simple interest :-

$$\longrightarrow \sf{simple \: interest = \dfrac{principal \times rate \times time}{100} }$$

2. Answer:

Principal = 18000

Time = 3/2 years

Rate = 10℅

A = P(1+r/200)²*³/²

= 18000(210/200)³

= 18000*(9261/8000)

= (166698/8000)

Amount = 20837.25

COMPOUND INTEREST = AMOUNT-PRINCIPAL

= (20837.25-18000)

= 2837.25

HOPE IT HELPS YOU BRO.