Question

How much would $\$ 500$invested at $4\% $interest compounded continuously be worth after $7$years?

Answer 1

Hint: Here we will use the concept of amount equals Principal times the mathematical constant (e) to the power of the rate of the interest (r) times the times in years (t) and will use the formula, $A = P{e^{rt}}$

Complete step-by-step answer:
First of all convert the given rate of percentage in the form of decimal.
$r = \dfrac{4}{{100}} = 0.04$
Now, use the formula $A = P{e^{rt}}$
Here, e stands for Napier’s number.
Place the given values in the above equation-
$A = 500{e^{0.04 \times 7}}$
The above equation when simplified can be written as –
$A = \$ 661.56$
This is the required solution.
So, the correct answer is “$A = \$ 661.56$”.

Note: Always convert the percentage rate of interest in the form of fraction or the decimals and then substitute further for the required solutions. Remember the difference between simple interest and compound interest and apply its concept wisely. Compound interest is the interest paid for the interest earned in the previous year. Be good in multiples and do simplification carefully.