You are saving money to buy a car. If you save $300 per month starting one month from now at an interest rate of 4%, how much will you be able to spend on the car after saving for 4 years?

Question

Quizplus · Accepted Answer

First, we need to calculate how much we will have saved in 4 years at an interest rate of 4%.

The formula for compound interest is:

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

Where:
A = the amount of money in the account after n years
P = the principal (starting) amount of money
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years

In this case, P = 0 (because we are starting from scratch), r = 0.04 (4% as a decimal), n = 12 (because the interest is compounded monthly), and t = 4 (because we are saving for 4 years). So we can plug these values into the formula:

A = 300(1 + 0.04/12)^(12*4)
A = 300(1.003333)^48
A = 300(1.18216)
A = $354.65 (rounded to two decimal places)

So after 1 month of saving, we will have $354.65 in the account. Then, for each subsequent month, we will add $300 to the account, and the interest will be compounded on the new balance each month.

To calculate the total amount saved after 4 years, we can use the formula:

A = P(1 + r)^t

Where:
A = the amount of money in the account after t years
P = the principal (starting) amount of money
r = the annual interest rate (as a decimal)
t = the number of years

In this case, P = $354.65 (the amount we have after the first month), r = 0.04 (4% as a decimal), and t = 4 (because we are saving for 4 years). So we can plug these values into the formula:

A = 354.65(1 + 0.04)^4
A = 354.65(1.16986)
A = $415.79 (rounded to two decimal places)

So after 4 years of saving, we will have $415.79 in the account. But we also need to subtract the amount that we have contributed ourselves:

300/month x 12 months/year x 4 years = $14,400

So the total amount that we can spend on the car is:

$415.79 - $14,400 = $15,587.88

Therefore, the best choice is A.

You Are Saving Money to Buy a Car