Question

pradeep invests a certain amount for 5 years at 12 percent compound intersetand at end of 2 years it amounts to rupees 10035.20.calculate the following . the interest earned in five year.​

Answer 1

Answer

As we are given with the amount of 2 years, rate of interest and time. We aren't giv n with the principle amount. So, first we should find the principle amount to find the interest earned in 5 years.

$\sf \dashrightarrow Amount = Principle \bigg( 1 + \dfrac{Rate}{100} \bigg)^{Time}$

$\sf \dashrightarrow 10035.20 = P \bigg( 1 + \dfrac{12}{100} \bigg)^{2}$

$\sf \dashrightarrow 10035.20 = P \bigg( \dfrac{100 + 12}{100} \bigg)^{2}$

$\sf \dashrightarrow 10035.20 = P \bigg( \dfrac{112}{100} \bigg)^{2}$

$\sf \dashrightarrow 10035.20 = P \bigg( \dfrac{112^2}{100^2} \bigg)$

$\sf \dashrightarrow 10035.20 = P \bigg( \dfrac{12544}{10000}$

$\sf \dashrightarrow P = \dfrac{10035.20}{\dfrac{12544}{10000}}$

$\sf \dashrightarrow P = 10025.20 \times \dfrac{10000}{12544}$

$\sf \dashrightarrow P = 0.8 \times 10000$

$\sf \dashrightarrow P = 8000$

Now, we can find the amount for 5 years.

Amount (5 years) :

$\sf \dashrightarrow Amount = Principle \bigg( 1 + \dfrac{Rate}{100} \bigg)^{Time}$

$\sf \dashrightarrow 8000 \bigg( 1 + \dfrac{12}{100} \bigg)^{5}$

$\sf \dashrightarrow 8000 \bigg( \dfrac{100 + 12}{100} \bigg)^{5}$

$\sf \dashrightarrow 8000 \bigg( \dfrac{112}{100} \bigg)^{5}$

$\sf \dashrightarrow 8000 \bigg( \dfrac{28}{25} \bigg)^{5}$

$\sf \dashrightarrow 8000 \bigg( \dfrac{28^5}{25^5} \bigg)$

$\sf \dashrightarrow 8000 \bigg( \dfrac{17210368}{9765625} \bigg)$

$\sf \dashrightarrow \dfrac{8000 \times 17210368}{9765626} = \dfrac{137682944000}{9765626}$

$\sf \dashrightarrow \cancel \dfrac{137682944000}{9765626} = 14098.732$

Now, we can find the compound interest.

Compound interest (5 years) :

$\sf \dashrightarrow Amount - Principle$

$\sf \dashrightarrow 14098.732 - 8000$

$\sf \dashrightarrow Rs.6098.732$

Hence, the compound interest for 5 years is ₹6098.732.