**Financial Calculators: Deferred Mortgages: Solving for Payment and Price**

**Finance Now, Pay Later!**

When a customer financing a loan or mortgage, and the customer can enjoy the benefits for a period of months prior to being required to make the first payment, we are dealing with a deferred mortgage. Interest is accrued from the beginning of the mortgage.

The procedures outlined on this blog entry can be applied to any financial calculator* with time value of money keys, such as the HP 12C and the HP 10bII+ (see source below).

* The procedure should be fine for most financial calculators. Check your manual for details.

**Deferred Mortgage: Finding The Monthly Payment**

Part 1:

Set the calculator to END mode.

N: Enter the number of deferred payments minus 1

I: Enter the interest rate of the loan

PV: Enter the borrowed amount as a negative number

PMT: Set to 0

Solve for FV

Part 2:

PV = FV from part 1 ( RCL FV, STO PV )

N: Enter the number of payments of the term

I = interest rate of the loan

FV: Enter the balloon payment as a negative number. If there is no balloon payment, enter 0.

Solve for PMT, this is your payment of the deferred mortgage.

Example 1:

A homeowner finances a house for $455,000.00. The mortgage lasts for 30 years at 2.86%. No payment is due for the first six months of the mortgage.

Part 1:

N: 6 -1 = 5

I: 2.86% annual rate, about 0.24% per month

PV: -455000.00

PMT: 0.00

FV = 460447.99

Part 2:

PV: 460447.99

N: 30* 12 = 360

I: 2.86% annual rate, about 0.24% per month

FV: 0.00

PMT = -1906.67

The monthly payment is $1,906.67.

Example 2:

A homeowner purchases a fixer-up property for $149,000.00. The buyer secures a 15-year mortgage at 4%. The end of the loan requires a $1,000.00 balloon payment but allows the buyer to defer the first payment for five months.

Part 1:

N: 5 - 1 = 4

I: 4% annual rate, about 0.33% per month

PV: -149000.00

PMT: 0.00

FV = 150996.62

Part 2:

PV: 150996.62

N: 15 * 12 = 180

I: 4% annual rate, about 0.33% per month

FV: -1000.00

PMT = -1112.84

Deferred Payment: Calculating the Price of the Mortgage

Part 1:

Set the calculator to END mode.

N: Enter the number of payments of the term

I: Enter the interest rate of the loan

PMT: Enter the payment as a positive number

FV: Enter the balloon payment as a positive number. If there is no balloon payment, enter 0.

Solve for FV

Part 2:

FV = PV from part 1 ( RCL PV, STO FV )

N: Enter the number of deferred payments minus 1

I = interest rate of the loan

Set PMT to 0

Solve for PV, this is your price of the deferred mortgage.

Example 3:

An owner enters a lease which requires at monthly payment of $495.00. The lease lasts for 8 years at 6.69%. There is no balloon payment at the end of the lease. The lease allowed the owner to defer the first required payments for three months. What is the value of the lease?

Part 1:

N: 8 * 12 = 96

I: 6.69% annual rate, about 0.56% per month

PMT: 495.00

FV: 0.00

PV = -36721.17

Part 2:

FV: -36721.17

N: 3 - 1 = 2

I: 6.69% annual rate, about 0.56% per month

Set PMT to 0

PV = 36315.13

The value of the lease is $36,315.13.

Example 4:

An owner executes a 30-year, 3% mortgage with the required payment of $1,005.85. The mortgage allows for the first payment to be deferred for six months. A $1,000.00 balloon payment is required. What is the price of the mortgage?

Part 1:

N: 30 * 12 = 360

I: 3% annual rate, 0.25% per month

PMT: 1005.85

FV: 1000.00

PV = -238983.97

Part 2:

FV: -238983.97

N: 6 - 1 = 5

I: 3% annual rate, 0.25% per month

Set PMT to 0

PV = 236018.94

The value of the lease is $236,018.94.

And that is how we work with deferred mortgages.

Source:

Greynolds Jr., Elbert B. and Aronofsky, Julius S. __ Practical Real Estate Financial Analysis: Using The HP 12C Calculator: A Step-by-Step Approach__ Real Estate Education Company: Dearborn Financial Publishing, Inc. 1983. ISBN 0-88462-378-5

Eddie

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