To calculate the monthly payment required to save the desired amount under the given​ conditions, use the savings plan formula​ below, which has been solved for the regular payment amount PMT. Recall that APR is the annual percentage rate expressed as a​ decimal, n is the number of payment periods per​ year, and Y is the number of years money is saved.

PMTequals=Upper A times StartFraction left parenthesis StartFraction APR Over n EndFraction right parenthesis Over left bracket left parenthesis 1 plus StartFraction APR Over n EndFraction right parenthesis Superscript left parenthesis nY right parenthesis Baseline minus 1 right bracket EndFractionA×APRn1+APRn(nY)−1

OK

The formula you're referring to is the savings plan formula, which calculates the monthly payment (PMT) needed to reach a desired future savings amount (A) over time, given an interest rate and the compounding periods. The formula can be written in a clearer format as follows:

\[
PMT = A \times \frac{\left( \frac{\text{APR}}{n} \right)}{\left( \left( 1 + \frac{\text{APR}}{n} \right)^{nY} - 1 \right)}
\]

Where:
- \( A \) = desired amount to save (future value)
- \( \text{APR} \) = annual percentage rate (as a decimal)
- \( n \) = number of compounding periods per year (typically, 12 for monthly payments)
- \( Y \) = number of years to save

### Steps to calculate PMT:
1. Divide the APR by \( n \) (to get the interest rate per period).
2. Add 1 to this value and raise it to the power of \( nY \) (which accounts for compounding over the total number of periods).
3. Subtract 1 from the result (this is the denominator of the formula).
4. Finally, divide the periodic interest rate \( \left( \frac{\text{APR}}{n} \right) \) by this denominator and multiply by the desired savings amount \( A \) to get the monthly payment.

Would you like to go through a specific example, or do you have values to plug into this formula?

---

Here are 5 questions you might find useful:
1. What is the exact desired savings amount (\(A\)) you wish to achieve?
2. What is the annual percentage rate (APR) in your scenario?
3. Over how many years (\(Y\)) do you plan to save the money?
4. How frequently will the savings compound (e.g., monthly, quarterly)?
5. Do you prefer a formula derivation breakdown?

**Tip:** Be mindful of the APR format. Always convert percentage rates into decimals by dividing by 100 (e.g., 5% becomes 0.05).

To calculate the monthly payment required to save the desired amount under the given conditions, use the savings plan formula below, which has been solved for the regular payment amount PMT. Recall that APR is the annual percentage rate expressed as a decimal, n is the number of payment periods per year, and Y is the number of years money is saved.

Discover how to calculate the monthly payment required to save a desired amount using the compound interest formula. This problem involves algebraic concepts and financial mathematics, covering the formula for calculating regular payments (PMT) based on APR, compounding periods, and years of saving. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation