Question

Lucas receives $90 and spends $30. He invests the remaining $60 for 3 years at 4% compound interest per year. Find the amount Lucas has after 3 years. Give your answer correct to 2 decimal places.

Answer 1

Given :

Invested amount : $60

Rate of interest : 4%

Time : 3 years

To find :

The amount with Lucas after 3 years.

Solution :

We can find the amount with Lucas by an appropriate formula

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

$\sf \dashrightarrow 60 \bigg( 1 + \dfrac{4}{100} \bigg)^{3}$

$\sf \dashrightarrow 60 \bigg( \dfrac{100 + 4}{100} \bigg)^{3}$

$\sf \dashrightarrow 60 \bigg( \dfrac{104}{100} \bigg)^{3}$

$\sf \dashrightarrow 60 \bigg( \dfrac{26}{25} \bigg)^{3}$

$\sf \dashrightarrow 60 \bigg( \dfrac{26^3}{25^3}\bigg)$

$\sf \dashrightarrow 60 \bigg( \dfrac{17576}{15265}\bigg)$

$\sf \dashrightarrow 12 \bigg( \dfrac{17576}{3053}\bigg)$

$\sf \dashrightarrow \dfrac{12 \times 17576}{3053} = \dfrac{210912}{3053}$

$\sf \dashrightarrow \cancel \dfrac{210912}{3053} = 69.08$

Hence, the amount with Lucas after 3 years is $69.08.