Question

I need to compare 2 mortgage options for this question. The amount and the duration of the mortgage are the same for both possibilities - $500,000.00 amortized over 25 years.

Option 1 – is a 5 year fixed rate mortgage. Payments will be made monthly and the annual interest rate is prime +1%.

Option 2 – is a 10 year fixed rate mortgage. Payments will be made bi-weekly and the annual interest rate is prime +2%.

Prime rate is currently 1.5%, and it’s going to increase by .25% per year for the next 10 years.

At the end of 10 years, how much will each option have paid down? For option 1 (with its 5 year term), assume a second 5 year term at the same interest rate (prime+1%)

*please show formulas used. Thank you!

Answer 1

As per the information given in the question:

Now there are two mortgage options. Let us decode them as given below:

Total Number of Payments:

Option-1: Payment is made monthly. So,12 nos. of payments in a year. Duration of the Mortgage is 25 Years.

                  So, Total No of payments = 25*12 = 300 Nos.

Option-2: Payment is made Biweekly (i.e.. 2 times in a month). So,12*2 = 24 nos. of payments in a year.    Duration of the Mortgage is 25 Years.

                  So, Total No of payments = 25*12*2 = 600 Nos.

Prime Interest Rate:

Current Prime rate is 1.5%. So for Year1 Prime rate will be 1.5%.

From Year 2 onwards Prime rate will increase by 0.25% per year for next 10 years. The same is calculated in the table below:

Option-1 Interest Rate:

Option-1 Interest rate = Prime rate + 1%. [Notes - Prime rate calculation already shown above]

Also in option-1 payment is made Monthly. 12 months in a year. So 12 payments in a year.

So, the effective interest rate will be Monthly interest rate = Annual Interest Rate / 12

The calculation will be same for 10 years as per information given in question. The same is calculated in the table below:

Option-2 Interest Rate:

Option-2 Interest rate = Prime rate + 2%. [Notes - Prime rate calculation already shown above]

Also in option-2 payment is made Bi-Weekly. 12 months in a year. 4 weeks in a month. Biweekly payment means (4 weeks / 2) = 2 payments in a month. So 12*2 = 24 payments in a year.

So, the effective interest rate will be Bi-Weekly interest rate = Annual Interest Rate / 24

The calculation will be same for 10 years as per information given in question. The same is calculated in the table below

Option-1 Payment Calculation:

The formula for Installment Payment for a mortgage is given below:

Installment Payment = M * [i(1 + i)^n]/[(1 + i)^n - 1]

                                                                                            ; where, M = "Mortgage Amount,"

                                                                                                             i = "per payment interest rate"

                                                                                                            n = "Total number of Payments"

Here, M = $ 500,000

             i = Monthly Interest rate [Note: As calculated in "Option-1 Interest Rate:" section]

             n = 300 [Note: As calculated in "Total Number of Payments:" section]

Based on the above formula and information the yearly payment calculation for 10 years is given below:

So, Total amount paid down in 10 Years under Option-1 = Sum (Payment Year1 : Payment Year 10)

                                                                                                     = $ 304,904.08

Option-2 Payment Calculation:

The formula for Installment Payment for a mortgage is given below:

Installment Payment = M * [i(1 + i)^n]/[(1 + i)^n - 1]

                                                                                            ; where, M = "Mortgage Amount,"

                                                                                                             i = "per payment interest rate"

                                                                                                            n = "Total number of Payments"

Here, M = $ 500,000

             i = Monthly Interest rate [Note: As calculated in "Option-2 Interest Rate:" section]

             n = 600 [Note: As calculated in "Total Number of Payments:" section]

Based on the above formula and information the yearly payment calculation for 10 years is given below:

So, Total amount paid down in 10 Years under Option-2 = Sum (Payment Year1 : Payment Year 10)

                                                                                                     = $ 338,067.42