If the interest on a sum of ₹ y at 4% per annum compounded annually for 2 years is ₹612, then the total amount payable at the end of the two-year period will be _____________.

Correct option is C

Given:

Principal amount = ₹y

Rate of interest = 4% per annum

Time = 2 years

Compound interest = ₹612

Concept Used:

Compound Interest formula:

A = P $$\left( 1 + \frac{r}{100} \right)^t$$​

A = 612 + y

Solution:

A is the total amount after interest,

P is the principal amount,

r is the rate of interest,

t is the time in years.

Applying Formula

$$612 + y = y\left( 1 + \frac{4}{100} \right)^2\\ \ \\612 + y = y\left(\frac{104}{100}\times\frac{104}{100} \right)\\ \ \\612 + y = y\left(\frac{26}{25}\times\frac{26}{25} \right)\\ \ \\\frac{612}y + \frac{y}{y} = \left(\frac{26}{25}\times\frac{26}{25} \right)\\ \ \\\frac{612}y = \frac{676}{625} – 1\\ \ \\\frac{612}y = \frac{676-625}{625}\\ \ \\\frac{612}y = \frac{51}{625}\\ \ \\\frac{612\times625}{51} = y$$​

12$$\times$$​625 = y

Y = 7500

Amount After 2 years = CI + P = 7500 + 612 = 8,112