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)
Calculate the rate of interest per compounding period (\(r\)):
\[r = \frac{\text{Rate of Interest}}{\text{Compounding Frequency}}\]
\[r = \frac{5\%}{12} = 0.004167\]
Determine the total number of compounding periods (\(nt\)):
\[nt = \text{Compounding Frequency} \times \text{Number of Years}\]
\[nt = 12 \times 30 = 360\]
Substitute the values into the formula and calculate the payment (\(PMT\)):
\[PMT = \frac{185,000 \times 0.004167}{1 - (1 + 0.004167)^{-360}}\]
\[PMT = \frac{770.95}{1 - (1.004167)^{-360}}\]
\[PMT = \frac{770.95}{1 - 0.2314}\]
\[PMT = \frac{770.95}{0.7686}\]
\[PMT = \$1,003.88\]
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:
Principal: \(P = \$185,000\)
Rate of Interest per Compounding Period: \(r = 0.004167\)