Question

Preeti purchased six years National savings certificate for₹1000. after six years she got ₹2015. find the rate of interest is compounded half-yearly.

[ Given that (2.015)^1/12 = 1.06012].

Answer 1

$\huge\blue{{ѕσℓυтισи}}$

$<b><i>$
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,

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

$= 2015 = 1000(1 + \frac{r}{100} )^{12}$

$\implies \: (1 + \frac{r}{100} )^{12} = \frac{2015}{1000} = 2.015$

$\implies \: (1 + \frac{r}{100}) = {2.015}^{ \frac{1}{12} } = 1.06012$

$\implies \: \frac{r}{100} = 1.06012 - 1 = 0.06012$

$r = 0.06012 \times 100 = 6.012$

∴ 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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