Question

A savings account was opened with an initial deposit and never touched again. An account that does not meet the minimum balance requirement is charged a service fee.

Assuming the account was open with an initial deposit below the minimum amount, the current account balance, B, is equal to the product of the initial deposit, I, and the quantity of the difference of 1 and the monthly service fee, f, raised to the power of n, the number of months since the account was open.

If an initial deposit of $2,713.00 is made to the account with a monthly service fee of 5%, what will be the value of B after 13 months? Round to the nearest cent.

Answer 1

To find the current balance B after 13 months with an initial deposit of $2,713.00 and a 5% monthly service fee, you multiply the initial deposit by 0.95 to the power of 13, resulting in a balance of approximately $1,392.64.

Step-by-step explanation:

The student's question involves using a given mathematical formula to find the current balance of a savings account affected by a monthly service fee. The formula provided states that the current balance B is equal to the initial deposit I times the quantity (1 - monthly service fee f) raised to the power of the number of months n. To calculate the current balance after 13 months, given an initial deposit of $2,713.00 and a monthly service fee of 5%, you'd perform the following calculation:

• Convert the percentage fee to a decimal: 5% = 0.05.
• Subtract the service fee from 1: 1 - 0.05 = 0.95.
• Raise the difference to the power of the number of months: 0.9513.
• Multiply the result by the initial deposit: $2,713.00 × 0.9513.

Using a calculator, this gives:

B = $2,713.00 × (0.9513) ≈ $2,713.00 × 0.5133421 ≈ $1,392.64

Rounded to the nearest cent, the value of B after 13 months is $1,392.64.

Answer 2

The equation we're given looks like:

`B=I(1-f)^n`
Substituting the information we're given, we have:

`B=2713(1-0.05)^1^3`
This is the same as:

`B=2713(0.95)^1^3`
which gives us an answer of $1392.70.