Question

If a savings account pays interest at 4% compounded quarterly, then the amount of $1 left

on deposit for 7 years would be found in a table using
a. 7 periods at 4%.
b. 7 periods at 1%.
c. 28 periods at 4%.
d. 28 periods at 1%.

Answer 1

In the context of a savings account with a 4% interest rate compounded quarterly, one would use 28 periods at 1% to find how much $1 deposited for 7 years would grow. The 1% represents the quarterly interest applied over 28 quarters in 7 years.

Step-by-step explanation:

In the context of a savings account with a 4% annual interest rate compounded quarterly, determining the future value of $1 deposited for 7 years involves understanding the principles of compound interest. With quarterly compounding, the interest rate is applied four times per year, resulting in a total of 28 compounding periods over the 7-year period (7 years x 4 quarters).

Since the interest is 4% annually, the quarterly interest rate is 1% (4% ÷ 4 quarters). This means that for each quarter, the deposit experiences a 1% growth due to interest.

To calculate the future value, one needs to consider the compounding effect over the 28 periods. Each quarter, the initial deposit grows by 1%, and this process is repeated for 28 quarters. The cumulative impact of these quarterly increments contributes to the overall growth of the initial deposit.

In summary, the theoretical approach involves recognizing the periodic application of a 1% interest rate over 28 quarters to determine the future value of the $1 deposit after 7 years. The concept of compound interest highlights the compounding effect over time, emphasizing the importance of the frequency of compounding periods and the associated interest rates.