Investment Payment Amount Calculator

What is an Investment Payment Amount?

An Investment Payment Amount is the regular payment made to an investment account to achieve a desired future value. This calculation helps investors understand how much they need to contribute periodically to reach their financial goals.

Formula for Calculating Investment Payment Amount

The formula to calculate the payment amount ($PMT$) is:

$$PMT=\frac{P\cdot r}{1-(1+r{)}^{-nt}}$$

Where:

• $PMT$ = Payment
• $P$ = Principal (Desired Amount Range - Down Payment + Closing Cost)
• $r$ = Rate of Interest / Compounding Frequency
• $nt$ = Compounding Frequency * Number of Years

Step-by-Step Calculation

1. Determine the principal ($P$): $$P=\text{Desired Amount Range}-\text{Down Payment}+\text{Closing Cost}$$ $$P=\mathrm{\$}200,000-\mathrm{\$}20,000+\mathrm{\$}5,000=\mathrm{\$}185,000$$
2. Calculate the rate of interest per compounding period ($r$): $$r=\frac{\text{Rate of Interest}}{\text{Compounding Frequency}}$$ $$r=\frac{5\mathrm{\%}}{12}=0.004167$$
3. Determine the total number of compounding periods ($nt$): $$nt=\text{Compounding Frequency}\times \text{Number of Years}$$ $$nt=12\times 30=360$$
4. Substitute the values into the formula and calculate the payment ($PMT$): $$PMT=\frac{185,000\times 0.004167}{1-(1+0.004167{)}^{-360}}$$ $$PMT=\frac{770.95}{1-(1.004167{)}^{-360}}$$ $$PMT=\frac{770.95}{1-0.2314}$$ $$PMT=\frac{770.95}{0.7686}$$ $$PMT=\mathrm{\$}1,003.88$$

Example Calculation

Let's calculate the payment amount for an investment with the following details:

• Desired Amount Range: $200,000
• Down Payment: $20,000
• Closing Cost: $5,000
• Rate of Interest: 5%
• Compounding Frequency: Monthly
• Number of Years: 30

Using the formula, we get:

1. Principal: $P=\mathrm{\$}185,000$
2. Rate of Interest per Compounding Period: $r=0.004167$
3. Total Number of Compounding Periods: $nt=360$
4. Payment Amount: $$PMT=\frac{185,000\times 0.004167}{1-(1+0.004167{)}^{-360}}$$ $$PMT=\mathrm{\$}1,003.88$$

Visual Representation

The green portion of the bar represents the calculated payment amount ($1,003.88) relative to the maximum possible value.