Question

Find the principal that will yield a compound interest of ₹1632 in 2years at 4% rate of interest per annum

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The principal that will yield a compound interest of ₹1632 in 2years at 4% rate of interest per annum is Rs 20000

Solution:

Given that,

Compound Interest = 1632

Number of years = 2

Rate of interest = 4 %

Let "p" represents the principal

Amount = Compound Interest + Principal

Thus  

Compound interest = Amount - Principal

$\begin{array}{l}{1632=\mathrm{P}\left[\left(1+\frac{r}{100}\right)^{2}\right]-\mathrm{P}} \\\\ {1632=\mathrm{P}\left[\left(1+\frac{4}{100}\right)^{2}\right]-\mathrm{P}}\end{array}$

$\begin{array}{l}{1632=\mathrm{P}\left[\left(1+\frac{1}{25}\right)^{2}\right]-\mathrm{P}} \\\\ {1632=\mathrm{P}\left[\frac{26}{25}\right]^{2}-\mathrm{P}}\end{array}$

$\begin{array}{l}{1632=\mathrm{P}\left[\frac{676}{625}\right]-\mathrm{P}} \\\\ {1632=\frac{676 \mathrm{P}-625 P}{625}}\end{array}$

On solving we get,

$\begin{array}{l}{1632 \times 625=51 \mathrm{P}} \\\\ {\mathrm{P}=\frac{1632 \times 625}{51}} \\\\ {\mathrm{P}=20000}\end{array}$

Thus Principal = Rs 20000

Learn more about Compound Interest

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