Question

Dan opened a savings account with $300 and was paid simple interest at an annual rate of 4%. When Dan closed the account, he was paid $72 in interest. How long was the account open for, in years? If necessary, refer to the list of financial formulas.​

Answer 1

6 years

Step-by-step explanation:

We can use the formula for simple interest to solve this problem:

Simple Interest = Principal x Rate x Time

where Principal is the initial amount invested, Rate is the annual interest rate, and Time is the duration of the investment.

Let's plug in the given values:

$72 = $300 x 0.04 x Time

Simplifying this equation, we get:

Time = $72 / ($300 x 0.04)

Time = 6 years

Therefore, the account was open for 6 years.

Answer 2

To determine the time period for which Dan's savings account was open, the simple interest formula was used. With an interest of $72, a principal of $300, and an annual rate of 4%, it was calculated that the account was open for 6 years.

Step-by-step explanation:

The student's question pertains to calculating the time period for which the savings account was open based on the simple interest earned. The formula for simple interest is Interest = Principal × Rate × Time, where Interest is the total interest earned, Principal is the initial amount deposited, Rate is the annual interest rate (expressed as a decimal), and Time is the number of years the account was open.

In this case, Dan earned $72 in interest on his initial deposit of $300 at an annual simple interest rate of 4% or 0.04. Using the simple interest formula I = P × R × T, we need to solve for T (Time in years). Substituting in the known values:

$72 = $300 × 0.04 × T

Divide both sides of the equation by ($300 × 0.04) to isolate T:

T = $72 / ($300 × 0.04) = $72 / $12 = 6

Therefore, the account was open for 6 years.