Final answer:
To determine how long it will take Linda Baer to save $7,755 with an initial amount of $5,000 invested at a 5% annual compound interest rate, we use the compound interest formula and solve for the variable t representing time in years.
Step-by-step explanation:
Linda Baer has saved $5,000 for a previously owned vehicle and wants to know how long it will take to afford a car that costs $7,755 if the money is invested in a CD with a 5% annual compounding interest rate.
To calculate the time needed, we use the formula for compound interest A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount ($5,000), r is the annual interest rate (5%), n is the number of times that interest is compounded per year (1 for annually), and t is the time in years.
First, we need to solve for t:
$7,755 = $5,000(1 + 0.05/1)^(1*t)
Simplifying the equation, we solve for t:
1.55 = (1.05)^t
To find t, we would take the logarithm of both sides:
log(1.55) = t * log(1.05)
t = log(1.55) / log(1.05)
Calculating this gives us the number of years Linda will have to wait until she has $7,755 saved to buy the car.