You're trying to save to buy a new $68,000 sports car. Currently, you have saved $36,840 which is invested at 4.9 percent annual interest. How many years will it be before you purchase the car, assuming the price of the car remains constant?

Question

Quizplus · Accepted Answer

Using the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

We want to solve for t, so we can rearrange the formula to isolate t:
t = (log(A/P) / log(1 + r/n)) / n

Plugging in the values given in the problem:
A = $68,000
P = $36,840
r = 4.9% = 0.049
n = 1 (compounded annually)

t = (log(68000/36840) / log(1 + 0.049/1)) / 1
t = 12.81 years (rounded to two decimal places)

Therefore, it will take approximately 12.81 years to save enough money to purchase the car. The answer is C.

You're Trying to Save to Buy a New $68,000 Sports