Question

Consider the following pool of mortgages:

• 100 fully amortizing mortgages
• Original balance $209,170
• Fixed rate interest at 2%
• Issued for 30 years with monthly payments

Assuming there are no prepayments, what do you predict the pool factor will be after 127 payments? Round your answer to two decimal points (e.g. if your answer is 1/3, enter 0.33).

Answer 1

Original Loan Balance = $209,170

Annual interest rate = 2%

Monthly Interest Rate = Annual Interest Rate / 12 = 2%/12 = 0.1667%

Loan Period = 30 years = 30*12 months = 360 months

The monthly loan payment can be calculated using the PMT function in spreadsheet

PMT(rate, number of periods, present value, future value, when-due)

Where, rate = Monthly Interest Rate = 0.1667%

number of periods = Loan Period = 360 months

present value = Loan Amount = $209,170

future value = 0

when-due = when is the payment made each month = end = 0

The monthly loan payment = PMT(0.1667%, 360, 209170, 0, 0) = -$773.13

Loan balance after 127 payments can be calculated using PV function in spreadsheet

PV(rate, number of periods, payment amount, future value, when-due)

Where, rate = Monthly Interest Rate = 0.1667%

number of periods = Remaining Loan Period = 360-127 months = 233 months

payment amount = monthly loan payment = -$773.13

future value = 0

when-due = when is the payment made each month = end = 0

Loan balance after 127 payments = PV(0.1667%, 233, -773.13, 0, 0) = $149,181.20

Pool Factor = Outstanding Loan Balance / Original Loan Balance = $149,181.20 / $209,170 = 0.71