PSAT Math Multiple-Choice Question 680: Answer and Explanation

Question: 680

The formula for annual compounded interest is A = P ^nt, where P is the initial amount invested, A is the future value of the initial amount, r is the annual interest rate expressed as a decimal, n is the number of times the investment is compounded each year, and t is the number of years the amount is invested. If an initial investment, P, is compounded once every 12 months, which expression is equivalent to the future value of the investment if its interest rate is 5% and if the money is invested for exactly 1 year?

• A. 0.05P
• B. 0.5P
• C. 1.05P
• D. 1.50P

Correct Answer: C

Explanation:

(C) First, let's identify all of the givens.

Since we're not provided a value for P, we will leave it as is in the formula.

We're also given that the interest is compounded once every 12 months. In other words, it's compounded once every year. Since n is the number of times the investment is compounded yearly, n = 1.

We're also told that the investment rate is 5%. Because r is the interest rate expressed as a decimal, .

We want to know A after 1 year, so t = 1.

Now plug everything into the equation:

Choice (C) is the answer.