Khloe invested $160 in an account paying an interest rate of 5.7% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 17 years?(1 point)

Question

Responses

$325
$325

$61,401
$61,401

$422
$422

$576

Answer 1

To calculate the amount of money in an account with continuous compounding, we can use the formula:

$$A=P{e}^{rt}$$

where:

• $A$ is the amount of money accumulated after time $t$,
• $P$ is the principal amount (the initial amount of money),
• $r$ is the annual interest rate (decimal),
• $t$ is the time the money is invested for in years,
• $e$ is the base of the natural logarithm, approximately equal to 2.71828.

In this case:

• $P=160$
• $r=5.7$
• $t=17$

Now we substitute the values into the formula:

$$A=160\cdot e^{0.057\cdot 17}$$

Calculating $0.057\cdot 17$:

$$0.057\cdot 17=0.969$$

Now we calculate $e^{0.969}$:

$$e^{0.969}\approx 2.634$$

Now we calculate $A$:

$$A\approx 160\cdot 2.634\approx 421.44$$

Rounding to the nearest dollar, the amount in the account after 17 years would be approximately:

$$\boxed{{\displaystyle 422}}$$