Question

Math of finance

Bob is paying 1184.87 in monthly mortgage payments. She wants to refinance her existing mortgage loan of $100,000 at 14% interest for 30 years that she obtained 4 years ago. Her mortgage officer informed her that he could get her a rate of 10% but the finance cost would include paying a prepayment penalty on the existing loan, which is equal to 6 months interest on the balance of the loan, plus a closing cost of $2000. Would it be worth if for Bob to refinance? Justify your answer.

Answer 1

First we will calculate the Outstanding loan balance of Bob loan:

Outstanding Balance = P* [(1 + r)" - (1+r) (1 + r) - 1

where, P = Loan Amount = $ 100,000

r = periodic Interest = 0.14/12 = 0.01166

n= no of periods = 30 years*12 months = 360

m = no of periods lapsed = 4 years *12 = 48

[(1 + 0.01166)300 – (1 +0.01166) 481 Outstanding Balance = 100000* (1 +0.01166) 300 - 1

Outstanding Balance = 100000* 65.084661 – 1.745007 65.084661 - 1

Outstanding Loan Balance = $ 98837.46

- Monthly payment = $1184.87

No of years left on loan = 30- 4 = 26 years

Total Interest on these 26 years= Total Payment in 26 years - current Loan balance

= ($1184.87*26 years*12 months)-$98837.46

= $ 270841.98

- Prepayment Penalty =6 months Interest on loan balance = $ 98837.46*14%*6/12

= $ 6918.62

Closing Cost = $ 2000

cost associated to refinance = $ 6918.62 + $ 2000 = $ 8918.62

Now, calculating the monthly payment of refinance loan:

EMI =P*r* (1+r)" (1+r) -1

where,P = Loan amount = $ 98837.46

r = periodic Interest = 0.10/12 = 0.00833

n= no of periods = (30-4) years*12 months = 312

EMI = 98837.46 * 0.00833 * (1 +0.00833) 312 (1 + 0.00833)312 - 1

EMI = 98837.46 * 0.00833 * 13.319465 13.319465 - 1

EMI = $ 890.50

Total interest over period of loan = ($ 890.50*312) - $ 98837.46

= $ 178,998.54

Total cost of new loan = $ 178998.54 + $8918.62

= $ 187917.16

As total cost of new loan is less than old loan, Bob should refinance.

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