Jasmine is leasing a car originally valued at $43,610. The lease is being financed with an interest rate of 7.33% compounded monthly with beginning of month payments of $524.

(a) How many payments will Jasmine have to make to repay the original value?

payment(s)

(b) How long, in months, will it take Jasmine to pay off the lease? (Hint: In an annuity due, payments are made at the beginning of each period.)

months)

This problem involves an **annuity due** (payments made at the beginning of each period) with monthly payments of $524, an initial car value of $43,610, and a monthly compounded interest rate of 7.33%.

To solve this, we will use the **annuity due formula** to determine the number of payments Jasmine must make:

\[
P = \frac{A(1 - (1 + r)^{-n})}{r}
\]

Where:
- $P$ is the present value of the lease (\$43,610),
- $A$ is the monthly payment (\$524),
- $r$ is the monthly interest rate (annual rate of 7.33%, compounded monthly),
- $n$ is the number of payments (this is what we are solving for).

Because the payments are at the beginning of the month, we will adjust the formula for an annuity due by multiplying the present value by $(1 + r)$.

Let me calculate that for you step by step.It seems the current formulation didn't provide a solution. I will try another approach to solve the equation step by step using logarithmic methods to handle the unknown $n$ in the annuity due formula.

Let me rework that calculation and provide a clearer solution.It appears there was a miscalculation. Let's correct the approach by revisiting the formula step by step. Specifically, I will correctly isolate the variables for the annuity due equation and compute $n$, the number of payments Jasmine must make.

Let me adjust the steps for a more accurate solution.To solve for the number of payments $n$, we'll use the formula for an **annuity due**. First, I'll reformulate the process clearly:

Given:
- Present value $P = 43,610$
- Monthly payment $A = 524$
- Annual interest rate $7.33\%$, compounded monthly
- Monthly interest rate $r = \frac{7.33\%}{12}$

The formula for **annuity due** can be rearranged and solved for $n$. I'll recompute this using the correct steps and isolate $n$ from the equation systematically. Please allow me to proceed with that.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you have any other questions or need further clarifications, feel free to ask!

Jasmine is leasing a car originally valued at $43,610. The lease is being financed with an interest rate of 7.33% compounded monthly with beginning of month payments of $524.

(a) How many payments will Jasmine have to make to repay the original value?

(b) How long, in months, will it take Jasmine to pay off the lease? (Hint: In an annuity due, payments are made at the beginning of each period.)

Find out how to calculate the number of payments Jasmine needs to make to pay off her car lease. This problem involves using the annuity due formula with a monthly compounded interest rate of 7.33%, a car value of $43,610, and monthly payments of $524. Ideal for students in Grades 11-12.

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