Question

Ms. Santoro is opening a one-year CD for $ 16,000. The interest is compounded daily. She is told by the bank representative that the annual percentage rate (APR) is 4.8%. What will be the value of the CD after one year?

Answer 1

After one year, the value of Ms. Santoro's one-year CD will be approximately $16,757.22.

Step-by-step explanation:

Ms. Santoro's CD is subject to daily compounding, which requires the application of the compound interest formula:

`\[ A = P * \left(1 + (r)/(n)\right)^(n * t) \]`

Where:

• A is the future value of the investment/loan, including interest.

• P is the principal amount (initial investment).

• r is the annual interest rate (in decimal form).

• n is the number of times that interest is compounded per unit
  `\(t\)`.

• 
  `\(t\)` is the time the money is invested/borrowed for in years.

In this case,
`\(P = $16,000\), \(r = 0.048\), \(n = 365\)` (daily compounding), and \(t = 1\) year.

Plugging in these values:

`\[ A = $16,000 * \left(1 + (0.048)/(365)\right)^(365 * 1) \]`

Calculating this expression yields the final value of Ms. Santoro's CD after one year, which is approximately $16,757.22.

This result highlights the impact of daily compounding, as it allows for the continuous accrual of interest on the principal amount throughout the year.

The higher the compounding frequency, the more frequently interest is added, leading to a higher overall return on the investment.

In this scenario, the daily compounding significantly contributes to the final value of the CD, showcasing the importance of understanding the compounding frequency when evaluating the growth of an investment.