Yield Maintenance Calculator

Formula

The formula to calculate yield maintenance is:

\[ YM = PVMP \cdot \left( \frac{IR}{100} - \frac{TY}{100} \right) \]

Where:

$ YM $ is the Yield Maintenance ($)
$ PVMP $ is the present value of all remaining mortgage payments on the loan ($)
$ IR $ is the interest rate of the loan (%)
$ TY $ is the treasury yield (%)

The present value of all remaining mortgage payments (PVMP) is calculated as:

\[ PVMP = \frac{1 - (1 + r)^{-n/12}}{r} \cdot B \]

Where:

$ r $ is the interest rate per month
$ n $ is the number of months remaining
$ B $ is the balance on the loan ($)

What is Yield Maintenance?

Yield maintenance is a type of prepayment penalty that investors attain to yield the same amount as if the borrower made all scheduled interest payments up until the maturity date.

Example

Let's say the interest rate (IR) is 5%, the treasury yield (TY) is 2%, the balance on the loan (B) is $1,000,000, and the number of months remaining (n) is 120. Using the formulas:

\[ r = \frac{5}{100 \cdot 12} = 0.004167 \]

\[ PVMP = \frac{1 - (1 + 0.004167)^{-120}}{0.004167} \cdot 1,000,000 \approx 933,390.33 \]

\[ YM = 933,390.33 \cdot \left( \frac{5}{100} - \frac{2}{100} \right) = 933,390.33 \cdot 0.03 \approx 28,001.71 \]

So, the yield maintenance (YM) is approximately $28,001.71.