Question

Ayanna is planning to buy a car. She currently has $3420 in a savings account. She needs at least a $6000 down payment. If her account earns 7% interest compounded continuously, will she have enough money in the account to buy the car in 2 years?

a. Yes, she'll have $13868
b. Yes, she'll have $6000
c. No, she'll have $5628
d. No, she'll have $3468

Answer 1

Using the formula for continuous compounding interest, Ayanna will have approximately $3935.43 in her savings account after 2 years, which is not enough to meet her $6000 down payment requirement for buying a car.

Step-by-step explanation:

Will Ayanna have enough money to make a $6000 down payment for a car after 2 years if she currently has $3420 in a savings account that earns 7% interest compounded continuously? To answer this, we can use the formula for continuous compounding interest, which is A = Pert, where P is the principal amount ($3420), r is the annual interest rate (0.07), t is the time in years (2), and e is the base of the natural logarithm (approximately 2.71828).

Calculating this we have:
A = 3420e(0.07)(2) = 3420 * e0.14 = 3420 * 1.150273 ≈ $3935.43

Since $3935.43 is less than the required $6000 down payment, the answer is No, Ayanna will not have enough after 2 years to make the down payment. She will have approximately $3935.43, which makes the correct answer choice (c) No, she will have $5628 incorrect. Therefore, Ayanna will not have enough money by a significant margin.