Question

This afternoon, instead of spending a gazillion dollars at Starbucks, you deposited $1,000 into a retirement savings account. The account will compound interest at 6 percent annually. You will not withdraw any principal or interest until you retire in 40 years. Which one of the following statements is correct?

A-The interest you earn in Year 6 will equal the interest you earn in Year 10.
B-The interest amount you earn will double in value every year.
C-The total amount of interest you will earn will equal $1,000 × .06 × 40.
D-The present value of this investment is equal to $1,000.
E-The future value of this amount is equal to $1,000 × (1 + 40).06.

Answer 1

The correct statement regarding the compounding of interest in a retirement savings account at 6 percent annually for 40 years is that the present value of this investment is equal to $1,000. The future value and the total amount of the interest earned are calculated using the compound interest formula, which takes into account the annual interest rate and the time the money is invested.

Step-by-step explanation:

The statement that is correct regarding the retirement savings account compounding interest at 6 percent annually for 40 years is: The present value of this investment is equal to $1,000. This is because the present value is the initial amount deposited into the account before any interest is compounded. The concept of profitable saving and compound interest illustrates the power of earning interest on interest over time, significantly increasing the future value of the original investment. However, it's important to note the following:

• The interest earned in different years will not be the same due to the nature of compound interest - it increases as the account balance grows.
• The interest amount does not double every year; it grows at a rate determined by the interest rate and the compound frequency.
• The total interest earned is not simply the product of the initial deposit, the annual rate, and the time period; it is calculated based on compound interest.
• The future value of the investment is not equal to $1,000 × (1 + 40).06 but is calculated using the compound interest formula.

To further understand the workings of compound interest, you can use the compound interest formula, which is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.