Finance

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Finance

Amount: A principal P placed at an annual rate of interest r for n years accumulates to an amount An as follows:

Simple interest: An = P(1+rn)

Compound interest: [pic]

Interest compounded q times per year: [pic]

Nominal and Effective Interest Rates: The rate of interest quoted in describing a given compound interest is called the “nominal rate.” The rate per year at which interest is earned during the year is called the “effective rate.” The effective rate i corresponding to the nominal rate r, is [pic]. Note that i ( r. If interest is paid only once per year, i.e., q = 1, then the nominal and effective rates are the same. Compounding interest more than once per year, i.e., q > 1, yields a larger effective rate. APR (annual percentage rate) is the nominal annual interest rate plus one-time fees and additional charges. Although APR is intended to represent the total cost of credit to the consumer, it understates the true (effective) rate. An announced APR of 12.99% compounded monthly (as with credit card debt) is effectively a rate of 13.78%.

Present or Discounted Value of a Future Amount: The present quantity P which in n years will accumulate to the amount An at the rate of interest r is:

Simple interest: [pic]

Compound interest: [pic]

Interest compounded q times per year: [pic]

Amount of an Annuity: If an annuity P is deposited at the end of each year, and interested, compounded annually, is paid on the accumulated deposit at the end of each year, the total amount N accumulated at the end of n years is

[pic]

N is called the amount of an annuity P.

Present Value of an Annuity: The total present amount P which will supply an annuity N at the end of each year for n years, beginning one year hence, (assuming that in successive years the amount not yet paid out earns interest at rate r, compounded annually) is

[pic]

Amount of a Sinking Fund: If a fixed investment N is made at the end of each successive year (beginning at the end of the first year), and interest paid at rate r, compounded annually, is paid on the accumulated amount of the investments at the end of each year, the total amount S accumulated at the end of n years is:

[pic]

S is called the amount of the sinking fund.

Note: These descriptions and formulas have been taken from Burington, R., “Handbook of Mathematical Tables and Formulas”