Question

Lynn deposits $9000 into a bank account. If the account has accumulated to $9383.40 in one year, determine the effective rate of interest during this year.

a. 4.26%

b. 3.15%

c. 4.84%

d. 4.38%

Answer 1

The effective rate of interest Lynn earned on her $9000 deposit over one year is 4.26%. This was determined by calculating the growth of her initial deposit to her final balance after one year.

Step-by-step explanation:

To determine the effective rate of interest on the bank account for the year, we can use the formula for the final account balance which includes interest. The final balance on an account is equal to the initial deposit plus the interest earned.

In Lynn's case, the initial deposit is $9000 and the final balance after one year is $9383.40. The formula to find the effective interest rate (r) can be set up as:

Final balance = Initial deposit × (1 + r)

$9383.40 = $9000 × (1 + r)

Now, dividing both sides by $9000 gives us:

1 + r = $9383.40 / $9000

Calculating the right side of the equation:

1 + r = 1.0426

To find the rate, subtract 1 from both sides:

r = 1.0426 - 1

r = 0.0426

Converting the decimal to a percentage gives us an effective rate of interest:

r = 4.26%

Therefore, the effective rate of interest Lynn earned on her deposit over one year is 4.26%, so the answer is option (a).