Question

what sum invested for 1½ years compounded half yearly at the rate of 4% per annum amounts to 132651​

Answer 1

Answer:

The sum of amount invested = 125000

Step-by-step explanation:

Given : Period T = 1.5 years

            Compounded frequency =  N = half yearly = 2

            Rate of interest R = 4%

           Compounded amount A = 132651

           Principle amount P = ?

Solution : Compounded amount A = P (1 + R/Nx100)^NT

             Substituting the given values, we get

             132651 = P x ( 1 + 4/2x100)^2x1.5

                          = P x (1 + 0.02)^3

∴                  P = 132651/1.02³

                      = 125000

Answer 2

 Given- We are given  Amount(A) = INR 1,32,651 , of money having rate of       interest (r) = 4% and time period(n)= 1.5 years.

To find- We have to find the principal.

Solution- We know that for compound interest,

             A= P [1+(r/100)]^{n}

⇒    P = A / [ 1+ (r/100)]^{n}

Here n = 3$\frac{1}{2}$ years and hence n = 3 as this interest is to be calculated half-yearly and there are 3 half-years.

Putting the values of A, n, r we get

⇒    P = 1,32,651 / $[1+\frac{4}{100} ]^{3}$ -------------(1)

 We solve the part inside the bracket separately,

$[1+ \frac{4}{100} ]^{3}$ = $[\frac{104}{100}] ^{3}$ = $[\frac{51}{50} ]^{3}$

Putting this value in (1), we get

⇒ P = 1,32,651 × $[\frac{50}{51}]^{3} }$$= \frac{(132651)(125000)}{132651}$ = 1,25,000.

Hence the principal is INR 1,25,000.