This problem involves calculating the number of payments required to reach a target balance in an account with a fixed interest rate. We will use the formula for the future value of an ordinary annuity (since payments are made at the end of each period).

The formula for the future value of an ordinary annuity is:

$FV = P \times \frac{(1 + r)^n - 1}{r}$

Where:

• $FV$ is the future value (the target balance) = $26,000
• $P$ is the payment per period = $350
• $r$ is the interest rate per period = annual rate / 12 months = 7.6% / 12 = 0.076 / 12 = 0.0063333
• $n$ is the number of payments (the unknown we need to solve for)

Rearranging the formula to solve for $n$:

$n = \frac{\ln\left(\frac{FV \cdot r}{P} + 1\right)}{\ln(1 + r)}$

Now, we can plug in the values:

$n = \frac{\ln\left(\frac{26000 \cdot 0.0063333}{350} + 1\right)}{\ln(1 + 0.0063333)}$

Let's calculate this step by step:

1. Calculate the term inside the logarithm.
2. Apply the logarithms to solve for $n$.

I'll now compute this. math

Given values

FV = 26000 P = 350 r = 0.076 / 12

Calculate the number of payments (n)

n = math.log((FV * r / P) + 1) / math.log(1 + r) nThe number of payments required to reach an account balance of $26,000 is approximately 61.07 payments.

Since the number of payments must be a whole number, you will need to make 61 payments to reach or exceed the target balance.

Would you like further clarification or details on how to approach similar problems?

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Here are some related questions for further exploration:

1. How would the result change if the interest rate were higher or lower?
2. What would the balance be after 50 payments with the same conditions?
3. How do you calculate the monthly payment needed to reach a target balance in a fixed number of periods?
4. How does compounding frequency affect the number of payments?
5. What is the difference between an ordinary annuity and an annuity due?

Tip: Always ensure that the interest rate is adjusted for the correct compounding period when solving for time in financial problems.