Question

find the amount and compound interest on 100000 compounded annually for 1 year 9 months at the rate 4 present per annum​

Answer 1

Given:

• Principal, P = 100000
• Time for interest, t = 1 year 9 months = $\sf{1\dfrac{3}{4}\;\;yrs}$
• Rate of interest per annum = 4 $\%$

To find:

• Compound amount, A =?
• Compound interest, CI =?

Formula required:

• Formula to calculate Compound Amount 'A' when time is in fraction say $\sf{t\dfrac{x}{y}\;\;yrs}$, Principal is 'P', rate of interest per annum is 'R'

$\boxed{\sf{A=P\bigg(1+\dfrac{R}{100}\bigg)^t\times \Bigg(1+\dfrac{\dfrac{x}{y}R}{100}\Bigg)}}$

• Amount = Principal + Compound interest

Solution:

Using Formula to calculate Compound amount

$\implies\sf{A=P\bigg(1+\dfrac{R}{100}\bigg)^t\times \Bigg(1+\dfrac{\dfrac{x}{y}R}{100}\Bigg)}$

$\implies\sf{A=100000\bigg(1+\dfrac{4}{100}\bigg)^1\times \Bigg(1+\dfrac{\dfrac{3}{4}\times4}{100}\Bigg)}$

$\implies\sf{A=100000\bigg(\dfrac{100+4}{100}\bigg)\times \bigg(1+\dfrac{3}{100}\bigg)}$

$\implies\sf{A=100000\bigg(\dfrac{104}{100}\bigg)\times \bigg(\dfrac{100+3}{100}\bigg)}$

$\implies\sf{A=10\times104\times103}$

$\implies\boxed{\boxed{\sf{A=107120\;}}}\:\:\:\star$

Now,

Calculating Compound interest

$\implies\sf{Amount=Principal + Compound\:interest}$

$\implies\sf{Compound\:interest=Amount - Principal}$

$\implies\sf{Compound\:interest=107120 - 100000}$

$\implies\boxed{\boxed{\sf{Compound\:interest=7120}}}\;\;\;\star$

Answer 2

Question

Find the amount and compound interest on 100000 compounded annually for 1 year 9 months at the rate 4 present per annum.