Question

Paul wants to buy a new car. Rather than take out a loan, he decides to save $200 a month in an account earning 3% interest compounded monthly. How much will he have saved up after 3 years?

Answer 1

To find out how much Paul will have saved up after 3 years, we can use the formula for compound interest. Using an initial savings of $200, an annual interest rate of 3%, compounded monthly, and 3 years, Paul will have approximately $6,972 saved up.

Step-by-step explanation:

To find out how much Paul will have saved up after 3 years, we can use the formula for compound interest:

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

Where:

• A = Amount saved after the specified time
• P = Principal amount (initial savings)
• r = Annual interest rate (as a decimal)
• n = Number of times interest is compounded in a year
• t = Number of years

In this case, P = $200, r = 0.03 (3% as a decimal), n = 12 (compounded monthly), and t = 3 years. Plugging in these values, we can calculate:

A = $200(1+0.03/12)^(12*3)

Simplifying the equation:

A = $200(1.0025)^(36)

Using a calculator, we find that Paul will have approximately $6,972 saved up after 3 years.