46.6k views
1 vote
What is the balance if

$500 is invested at 8% compounded quarterly after a period of
years?

a. $605. 90

b. $605. 90

c. $609. 50

d. $690. 50

e. none of the options display the

1 Answer

2 votes

Final answer:

The balance of $500 invested at an 8% interest rate compounded quarterly cannot be determined exactly without knowing the number of years. If, for example, we assume the money is invested for 3 years, the formula yields a balance of $634.12, not matching any of the provided options.

Step-by-step explanation:

To calculate the balance after a certain period with compound interest, we use the compound interest formula:
A = P(1 + r/n)^(nt), where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for

In this particular case, an initial investment of $500 at an 8% annual interest rate, compounded quarterly, means we use n = 4 (since interest is compounded quarterly). However, we're missing the number of years (t) the money is invested from the question provided. If, for example, the investment was for 3 years (which we'll assume for our calculations), the balance can be calculated as follows:

A = 500(1 + 0.08/4)^(4*3)
A = 500(1 + 0.02)^12
A = 500(1.02)^12
A = 500 * 1.26824
A = $634.12

Without the number of years specified, we cannot determine the exact balance, and thus none of the options provided would be correct. As for the reference to a total of $115.76, this seems to be based on a different principal amount and might not be directly relevant to the question at hand.

User Buzzet
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories