Financial calculator

In this post we will review the calculation formulas of more important.

SIMPLE INTEREST:  Interest is only calculated on the nominal.

                                           in years                           in months                             in days

where I is the interest calculated
          Co is the initial capital
          r is the annual simple interest rate.

And the formula to calculate the final amount to be returned:

                                                                                        in days

where CF is the Final Capital.

COMPOUND INTEREST:  The interest is added to calculate to the nominal in order to calculate new interests.

where n = number of years.
          k = number of times that interest is compounded in a year.

i / k represents the interest rate that applies to each compounding period.
n x k represents the times that there are to capitaliza interest over the life of the loan.

SIMPLE DISCOUNT RATE:  Present value of future incomes.

SIMPLE TRADE DISCOUNT RATE:  Present value of future incomes.  It is ussually applied by banks in business discount.

where Coco is the value of the Capital at present value using a discount rate.

COMPOUND DISCOUNT:  Present value of future incomes, where the interest is capitalized. 

Annual Percentage Rate (APR or TAE in Spanish):  It is the transformation of a compound interest where interest is capitalized k times a year, into an annual rate simple. 

 Example:  What is the APR on a loan with an annual interest rate of 8,5% if interest is capitalized daily?

The APR is 8,87%.

Internal Rate of Return (IRR):  is the interest rate that equates positive and negative incomes in different periods of time.

 where Dk are disbursements made in year k, and Rk are reimbursements received in year k.

NET PRESENT VALUE (NPV or VAN in Spanish):  is the sum of all disbursements and repayments of investment discounted to the current period at an interest rate.

Mortgage Payment or Instalement:  To calculate the amount to be paid for a loan (either monthly, annually or at intervals of k times a year), we will apply the formula:

where Co is the nominal of the loan, n is the number of years, and k is the number of times is capitalized per year.

Perpetuity:   It is a perpetual annuities compound interest rate.  What annual income (P) I would indefinitely get with an initial capital Co, at a compound interest rate r?

And if I want a perpetual income that grows at a rate g, what is the amount to deposit today?

By Miguel Angel Aisa Alcaine