Question

Ethan‘s bank account listed a balance of $328.80. He originally opened the account with a $200 deposit and a simple interest rate of 4.6% If there were no deposit or withdrawals, how long ago was the account opened

Answer 1

To find out how long ago Ethan opened his account, we use the simple interest formula I = PRT to calculate the interest and solve for time. With $128.80 in interest, a $200 initial deposit, and a 4.6% rate, the account was opened 14 years ago.

Step-by-step explanation:

Ethan wants to find out how long ago he opened his bank account based on the growth of his initial deposit with simple interest. To solve this, we will calculate the simple interest that Ethan's account has accrued and then use that information to find the time period.

The formula for calculating simple interest is given by I = PRT, where I is the interest, P is the principal amount, R is the rate of interest, and T is the time in years. Ethan's current balance is $328.80, and he made an initial deposit of $200. Therefore, the interest accrued is $328.80 - $200 = $128.80.

Using the simple interest formula:

• I = Simple interest = $128.80
• P = Principal = $200
• R = Interest rate per year = 4.6% or 0.046
• T = Time in years (this is what we are solving for)

Substitute these values into the formula:

$128.80 = $200 × 0.046 × T

Now, solve for T:

T = $128.80 / ($200 × 0.046)

T = $128.80 / $9.2

T = 14 years

Ethan's account was opened 14 years ago.