$900 is deposited in an account with 4% interest rate, compounded continuously. What is the balance after 10 years? F = $[?]

Question

asked Feb 10, 2024 160k views

1 Answer

Kyle Barron · Answer 1 · 2024-02-14T15:21:27+0000

Answer:

$\$1342.64$

Explanation:

We can represent the value
of a quantity
compounded continuously for
years at
rate of interest as:

$A = P\cdot e^(rt)$

This formula uses the mathematical constant
(approx. 2.72), which is the theoretical limit for continuous compounding.

Plugging the given values into the formula:

$A = \$900 \cdot e^((0.04 \, \cdot \, 10))$

We can now solve for
.

↓ simplifying
's exponent

$A = \$900 \cdot e^(0.4)$

↓ plugging into a calculator

$A \approx \$1342.64222788$

↓ rounding to the nearest cent

$\boxed{A \approx \$1342.64}$