Refinancing loans with a penalty clause

As interest rates drop it can be useful to refinance a loan.

To decide whether refinancing a loan is profitable the savings due to the lower rate should be compared to the cost of refinancing.

Example

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A couple borrows $75,000 to be repaid with monthly payments over 20 years at 9 % compounded quarterly. Their contract stipulates a penalty in case of early repayment equal to 3 monthly payments.

After 10 years and 3 months they can refinance at 7.5 % compounded quarterly.

Should they refinance?

Step 1: Calculate the monthly payment and the balance after 123 months for the original loan to find the total sum to be refinanced.

Calculation Amortization  
     
Input Nominal annual rate: 9 %
  Interest is compounded: quarterly
  Payments are made: monthly
  Number of payments: 240
  Present value: 75.000
     
Result Periodic payment: 671.58
Details Balance after the 123rd period: 52,333.62

Answer: $52,333.62 + (3 x $671.58) = $54,348.36.

Step 2: Calculate the monthly payment for the new loan to be able to compare it to the original monthly payment.

Calculation Amortization  
     
Input Nominal annual rate: 7.5 %
  Interest is compounded: quarterly
  Payments are made: monthly
  Number of payments: 117
  Present value: 54,348.36
     
Result Periodic payment: 654.95

Conclusion

The couple should refinance as for the remaining 117 months they will pay $671.58 - $654.95 = $16.63 less with a total saving of 117 x $16.63 = $1,945.71.

 

Related topics

Combining calculations
Amortization