Question

mei deposits $5,000 in an account that earns 4% compound interest each year.
use technology to determine when the account will reach $10,000.

select from the drop-down menu to correctly complete the sentence.

the account will reach $10,000 in ____ years.
options: 13, 17, 18, 25

Explanation:

Step1: Recall compound interest formula

The annual compound interest formula is $A = P(1+r)^t$, where:

• $A = 10000$ (target amount),
• $P = 5000$ (principal deposit),
• $r = 0.04$ (annual interest rate),
• $t$ = time in years (unknown).

Step2: Substitute values into formula

$$10000 = 5000(1+0.04)^t$$

Step3: Simplify the equation

Divide both sides by 5000:
$$2 = (1.04)^t$$

Step4: Solve for t using logarithms

Take natural log of both sides:
$$\ln(2) = t\ln(1.04)$$
Rearrange to solve for $t$:
$$t = \frac{\ln(2)}{\ln(1.04)}$$

Step5: Calculate the value

Using technology, $\frac{\ln(2)}{\ln(1.04)} \approx 17.67$, which rounds to 18 years.

Answer:

18