Question

Which of these options best represents the amount of time (t) in years that must pass before the certificate of deposit (CD) will have a value of $5000 in the future, given the equation 5000 = 4800 *(1 + 0.03)^t?

A) t = 5
B) t = 10
C) t = 15
D) t = 20

Answer 1

To find out how many years it will take for the CD to be worth $5000, we solve the equation 5000 = 4800 * (1 + 0.03)^t, which results in approximately 1.405 years. Since this is not an available option, we consider rounding to the nearest whole year, which gives us the closest answer A) t = 1.

Step-by-step explanation:

The student has presented the equation 5000 = 4800 * (1 + 0.03)^t which is used to calculate the amount of time (t) it will take for a certificate of deposit (CD) to reach a future value of $5000, given that the current value is $4800 and the interest rate is 3% compounded annually.

To solve for 't', we will rewrite the equation as:

• 5000 / 4800 = (1 + 0.03)^t
• 1.0416667 = (1.03)^t

Now, we take the logarithm of both sides to solve for 't':

• log(1.0416667) = t * log(1.03)
• 0.0180434 = t * 0.0128372
• t = 0.0180434 / 0.0128372
• t = 1.405

So, t is approximately 1.405 years. However, since this option is not available in the multiple-choice answers, we must either re-evaluate our calculation or consider other factors such as rounding or the precision of the answer. If we apply rounding to the nearest whole year, it would be closest to option A) t = 1.