**Chapter 13**

Appraisal Mathematics and Real Estate Finance

**Compounding**

## u Future
value of a lump sum

## u Future
value of an annuity

## u Sinking
fund

**Discounting**

## u Present
value of a lump sum

## u Present
value of an annuity

## u Uneven cash
flows

## u Payments in
advance

**Calculating a Mortgage Payment**

## u A mortgage
payment calculation is a present value of an annuity problem.

## u Enter the
payments per year (P/YR)

## u Enter the
number of years (xP/YR)

## u Enter the
annual interest rate (I/YR)

## u Enter the
loan amount (PV)

## u Solve for
Payment (PMT)

**Mortgage Payment Example**

## u What is the
monthly mortgage payment on a 30 year, $100,000 loan at 12% annual interest?

## u Enter the
payments per year (12 P/YR)

## u Enter the
number of years (30 xP/YR)

## u Enter the
annual interest rate (12 I/YR)

## u Enter the
loan amount (100000 PV)

## u Solve for
Payment (PMT) Display shows 1028.61

**Morgtgage Buydown Calculation**

## u First
compute the payment required at the market terms

## u Next
compute the payment required at the buydown rate.

## u Subtract
the two to determine the amount of the buydown savings.

## u Discount
the buydown savings at the market interest rate for the duration of the
savings.

**Buydown Calculation Example**

## u What is the
amount the bank would charge to buydown the monthly mortgage payment on a 30
year, $100,000 loan from 12% annual
interest to 11%?

## u First
compute the payment required at the market terms (1028.61)

## u Next
compute the payment required at the buydown rate (952.32)

## u Subtract
the two to determine the amount of the buydown savings. (1028.61 - 952.32 =
76.29)

## u Discount
the buydown savings at the market interest rate for the duration of the
savings. (76.29=PMT, I/YR=12, 30xP/YR, solve for PV. Display shows 7416.79)

**Mortgage Mathematics**

## u Mortgage
Payments

## u Computation
of APR

## u Computation
of Buydown amount