Question

You are trying to save up to buy the new iPhone 6 which is supposed to come out 18 months from now. You put $300 into a savings account that yields 3.6% annually. If the phone is going to coast $345 will you have enough money to buy it? Please help. I do not understand this problem.

A. Yes
B. No

Answer 1

After calculating the future value of a $300 investment at 3.6% annual interest over 18 months, the amount available will be $316.37, which is not enough to purchase the iPhone 6 at $345. Therefore, the answer is B. No.

Step-by-step explanation:

The student's question involves calculating the future value of an investment using the concept of compound interest to determine if they will have enough money to buy an iPhone 6 in 18 months. The investment is $300 with an annual interest rate of 3.6%. To solve this, we'll use the formula for compound interest:

FV = P(1 + r/n)^(nt)

Where FV is the future value, P is the principal amount ($300), r is the annual interest rate (3.6% or 0.036), n is the number of times that interest is compounded per year (assumed to be 1 since not specified), and t is the time in years (1.5 years for 18 months).

Plugging the values into the formula gives us:

FV = 300(1 + 0.036/1)^(1*1.5)

FV = 300(1 + 0.036)^(1.5)

FV = 300(1.036)^(1.5)

FV = 300(1.054576)

FV = 316.3728

Since the future value of $316.37 is less than the cost of the iPhone 6 at $345, the answer is B. No, the student will not have enough money to buy the iPhone after 18 months with the given savings plan.