Loans with adjustable rates

Some loan contracts stipulate that after a certain period of time payments will be adjusted to the new prevailing interest rate.

The following example shows you how you can calculate the new periodic payments when the interest rate changes.

Example

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John purchased a house and signed a mortgage contract for $95,000 to be paid in monthly installments over 20 years at 7.5 % compounded monthly. The contract stipulates that after 5 years the mortgage will be renegotiated at the new prevailing interest rate.

After 5 years the interest rate drops to 6.9 % compounded monthly.

What will be the new monthly payment and what will be the difference?

Step 1: Calculate the initial monthly payment and the balance after 5 years.

Calculation Amortization  
     
Input Nominal annual rate: 7.5 %
  Interest is compounded: monthly
  Payments are made: monthly
  Number of years: 20
  Present value: 95,000
     
Result Periodic payment: 765.31
Details Balance at the end of the fifth year: 82,556.99

Answer: The initial monthly payment is $765,31 and after five years the balance is $82,556.99.

Note that in 5 years, with payments totalling 60 x $765.31 = $45,918.60 only $95,000 - $82,556.99 = $12,443.01 of principal has been repaid.

Step 2: Calculate the new monthly payment for the remaining 15 years with the obtained balance and the new interest rate.

Calculation Amortization  
     
Input Nominal annual rate: 6.9 %
  Interest is compounded: monthly
  Payments are made: monthly
  Number of years: 15
  Present value: 82,556.99
     
Result Periodic payment: 737.44

Answer: The new monthly payment is $737,44.

Conclusion

John's monthly mortgage payment will fall by $765.31 - $737.44 = $28.07.

 

Related topics

Combining calculations
Amortization