Financial Toolbox

Annuities

Several toolbox functions deal with annuities. This first example shows how to compute the interest rate associated with a series of loan payments when only the payment amounts and principal are known. For a loan whose original value was $5000.00 and which was paid back monthly over four years at $130.00/month

• Rate = annurate(4*12, 130, 5000, 0, 0)
  

The function returns a rate of 0.0094 monthly, or approximately 11.28% annually.

The next example uses a present-value function to show how to compute the initial principal when the payment and rate are known. For a loan paid at $300.00/month over four years at 11% annual interest

• Principal = pvfix(0.11/12, 4*12, 300, 0, 0)
  

The function returns the original principal value of $11,607.43.

The final example computes an amortization schedule for a loan or annuity. The original value was $5000.00 and was paid back over 12 months at an annual rate of 9%.

• [Prpmt, Intpmt, Balance, Payment] = ...
          amortize(0.09/12, 12, 5000, 0, 0);
  

This function returns vectors containing the amount of principal paid,

• Prpmt = [402.76  405.78  408.82  411.89  414.97  418.09 
           421.22  424.38  427.56  430.77  434.00  437.26]
  

the amount of interest paid,

• Intpmt = [34.50  31.48  28.44  25.37  22.28  19.17 
            16.03  12.88   9.69   6.49   3.26   0.00]
  

the remaining balance for each period of the loan,

• Balance = [4600.24  4197.49  3791.71  3382.89  2971.01 
             2556.03  2137.94  1716.72  1292.34   864.77 
              434.00    0.00]
  

and a scalar for the monthly payment.

• Payment = 437.26
  

Depreciation

Pricing and Computing Yields for Fixed-Income Securities