Question

Ranu purchase one six years National saving certificate for rs 1000 . after six years she got rs 2012.2 . find the rate of interest, if the internet is compound half yearly​

Answer 1

Answer:

Principal (p) = ₹ 1000,

Amount (A) = ₹ 2015,

Time (n) = 6 years.

When the interest is compounded half-yearly, then the time is 12 half-years.

let the half-yearly rate of interest be r%.

Then,

\begin{gathered}\bold{A \: = P(1 + \frac{r}{100}) ^{n} } \\\end{gathered}A=P(1+100r)n

\begin{gathered}= 2015 = 1000(1 + \frac{r}{100} )^{12} \\\end{gathered}=2015=1000(1+100r)12

\begin{gathered}\implies \: (1 + \frac{r}{100} )^{12} = \frac{2015}{1000} = 2.015 \\\end{gathered}⟹(1+100r)12=10002015=2.015

\begin{gathered}\implies \: (1 + \frac{r}{100}) = {2.015}^{ \frac{1}{12} } = 1.06012 \\\end{gathered}⟹(1+100r)=2.015121=1.06012

\begin{gathered}\implies \: \frac{r}{100} = 1.06012 - 1 = 0.06012 \\\end{gathered}⟹100r=1.06012−1=0.06012

\begin{gathered}r = 0.06012 \times 100 = 6.012 \\\end{gathered}r=0.06012×100=6.012

∴ Rate of interest per annum = 2r% = 2×6.012%

= 12.024% ≌ 12℅

∴ Hence, the required rate of interest is 12℅ p.a

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