Question

A sum of 25,000 invested at 8% p.a. compounded semi-annually amounts to 28,121.60. Find the
time period.
​

Answer 1

Cᴏʀʀᴇᴄᴛ Qᴜᴇsᴛɪᴏɴ :-

• A sum rupees 25000 invested at 8% per annum compounded semi annually amount to 28121.60.Find the time period.

Gɪᴠᴇɴ :-

➨ Principal amount (P) = 25000

➨ Rate of interest = 8℅ compounded semi annually

➨ Amount = 28121.60

Tᴏ Fɪɴᴅ :-

• The time period.

Sᴏʟᴜᴛɪᴏɴ :-

• Formula for,

$\red{\underline{{\bf Compound \: interest \: for \: semi \: annually :-}}}$

${\boxed{{\bf{A = P(1 + \frac{r}{200})^{2n} }}}}$

$\sf\large\green{⇝28121.60 = 25000(1 + \frac{8}{200}) ^{2n} }$

$\sf\large\green{⇝ \frac{28121.60}{25000} = (1 + \frac{1}{25} ) ^{2n} }$

$\sf\large\green{⇝ \frac{28121.60}{25000} = \frac{26}{25} ^{2n} }$

$\sf\large\green{ ⇝1.124 = \frac{676}{625} ^{n} }$

$\sf\large\green{ ⇝n = 1.5 \: approximately }$

${\boxed{{\bf{∴The \: time \: period = 1.5 \: years}}}}$

Answer 2

$\huge\frak{\underline{\underline{\red{Answer}}}}$

➡ Time period = 1.5 years