Question

What principal will amount to ₹17576 IN 18 MONTHS AT A RATE OF INTEREST 8 %Per annum compounded half yearly

Answer 1

Given:

An amount of ₹17576 in 18 months at a rate of interest 8 % p.a. compounded half-yearly

To find:

The principal

Solution:

Let's assume "P" represents the principal.

Amount, A = Rs. 17576

The rate of interest, R = 8% p.a.  

The no. of years,

n = 18 months = $\frac{18}{12} \: years = 1.5 \:years$

The formula to find the amount when the interest is compounded half-yearly is:

$\boxed{\bold{A = P [ 1+ \frac{\frac{R}{2}}{100} ]^2 ^ n }}$

Now, on substituting the given values in the formula above, we get

$17576= P [ 1 + \frac{\frac{8}{2}}{100} ]^2 ^\times ^ 1^.^ 5 }}$

$\implies 17576 = P [1 + \frac{4}{100} ]^3$

$\implies 17576 = P [1 + \frac{1}{25} ]^3$

$\implies 17576 = P [ \frac{26}{25} ]^3$

$\implies P = 17576 \times [ \frac{25}{26} ]^3$

$\implies \bold{P = 15625}$

Thus, the principal is → ₹ 15625.

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