Question

Suppose the APR is 6% when you purchased your house 10 years ago. The house price is 300K but the down payment is 20% and the rest you borrowed from the bank.

1.) What is your monthly mortgage payment if you applied for a 30 year mortgage.

2.) How much do you still owe to the bank if you want to pay your mortgage off today?

3.) You are considering refinancing your mortgage rate but you still want to pay off all your mortgage in 20 years. The bank quotes you the 20 year mortgage rate is 5% but the refinance cost you $5,000 transaction fee. Considering the potential interest saving, is it worthy for you to do refinance or not today?

Show calculations

Answer 1

1)

2)

At the end of 10 years, loan outstanding is $200845.74. This is the amount that is needed to be paid today as a balloon payment.

This calculation can be done by preparing an amortization period

The below screenshot shows how to create an amortization period. The opening balance tells the loan outstanding at the start of the period, payments made is the monthly mortgage payments made, interest paid is the part of monthly payments that goes towards paying interest and loan paid is the part of monthly payments towards loan payment. The closing balance shows the amount of loan remaining at the end of the period. The closing balance is the opening balance for the next period. The periods represent each month. For a 10 year duration we need to extend this table for 120 periods.

3)

Refinancing if done, is for the loan outstanding at the end of 10 years; i.e. $200,845.74

The calculation is again done using an amortization table. We calculate the savings in interest payments by taking the difference in the interest paid over the old rate for the remaining time and the interest paid with the new rate.

Total interest paid with the new rate for 20 years = $117272.58

Total interest paid with the old rate for last 20 years= $144,495.36

Savings in interest = 144495.36 - 117272.58 = 27,222.78

Opportunity cost of $5,000 used for refinancing at 5% per annum compounded monthly = 5000*(1+.42%)^240 = $13671.69

Total savings from refinancing = 27222.78 - 13671.69 = $13551.09