Question

Find compound interest
24000 for 1 year 146 days at 15/2%rate compounded annually ?

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Answer 1

Given :

Principle (P) = Rs. 24000

Time (n) = 1 year 146 days

Rate (R) = $\frac{15}{2}$%

To Find :

Compound Interest

Solution :

Time (n) = 1 year  + 146 days

             = 365 days + 146 days

             = 511 days

             = $\frac{511}{365}$

             = 1.4 years

We know, Compound Interest (CI) = P[$(1 + \frac{R}{100} )^{n}$ - 1]

or,                        CI  = 24000[$(1 + \frac{15}{2 * 100})^{1.4}$ - 1]

or,                        CI  = 24000[$(1 + \frac{7.5}{100} )^{1.4}$ - 1]

or,                        CI  = 24000[$(1 + \frac{7.5}{100} ) ( 1 + \frac{7.5 * 0.4}{100} )$ - 1]

or,                        CI  = 24000[(1.075)(1.03) - 1]

or,                        CI  = 24000[ 1.10725- 1]

or,                        CI  = 24000[0.10725]

or,                        CI  = 24000×0.10725

∴                          CI  = Rs. 2574

∴ Compound interest on Rs. 24000 for 1 year 146 days at $\frac{15}{2}$ % rate compounded annually is Rs. 2574.

   

Answer 2

Answer:

$2574 .$

Step-by-step explanation:

Given: Principle (P) = Rs 24000, time$(n)=1$ year 146 days

Rate $(\mathrm{R})=\frac{15}{2} \%$

To Find : Compound Interest.

First convert time in years as:

Time $(n)=1$ year$+146$ days

             $\begin{aligned}&=1 \text { years }+\frac{146}{365} \text { years } \\&=1+0.4 \text { years} \\&=\mathbf{1 . 4} \text { years }\end{aligned}$

Also, we know that compound Interest (CI) $=\mathrm{P}\left[\left(1+\frac{R}{100}\right)^{n}-1\right]$

$\begin{aligned}&\mathrm{Cl}=24000\left[\left(1+\frac{15}{2 * 100}\right)^{1.4}-1\right] \\&\mathrm{Cl}=24000\left[\left(1+\frac{7.5}{100}\right)^{1.4}-1\right]\end{aligned}$

$\mathrm{Cl}=24000\left[\left(1+\frac{7.5}{100}\right)\left(1+\frac{7.5 * 0.4}{100}\right)-1\right]$

$\mathrm{Cl}=24000[(1.075)(1.03)-1]$

$\mathrm{Cl}=24000[1.10725-1]$

$Cl = Rs. 2574$

Hence, compound interest on Rs. $\mathbf{2 4 0 0 0}$ for 1 year 146 days at $\frac{15}{2} \%$ rate compounded annually is Rs. $2574 .$

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