Chapter 14 
Compound Interest Calculations
(Compound Growth Calculations)

Previous:  14- Indirect Use of Compound Interest Formula, Backward, More Examples

4  Review and Further Notes

In money matters dealing with the compound interest formula, we can ask for the final compounded amount given by the direct use of the formula, but we can also ask for the other three quantities. That is, we may solve for the principal, for the interest rate or for the number of compounding periods. The compound interest formula can be viewed as one relationship between four quantities, anyone of which can be solved for or expressed in terms of the other three. In particular, the compound interest formula and equation A = P(1+i)ⁿ involves four quantities. When any three are known, the fourth can be found. The easiest quantity to find is A. Given the three numbers and quantities P, i and n, you can find the final amount A by the direct use of the formula. But by indirect use of the compound interest formula, that is by changing or manipulating it, given any three of the four quantities A, P, i and n, we can calculate the fourth. From the compound interest formula

A = P(1+i)n

in its usual form, we can obtain formulas for P, i and n. Their description follows.

 

• The so-called present value formula

  P = A (1+i)n

  This present value formula says what amount (or principal) P will grow to the amount A in n periods time if the interest rate is i. Vocabulary: the amount P is called the present value of the final amount A. Further the amount A is called the future or maturity value of P at the end of the n-th period.
• the interest rate formula

  i = é ê ë A P ù ú û 1/n                  [n] / -1 =       /            Ö __ A P   -1.

 

• A nameless formula for the exponent (or power) n. From the compound interest formula, we can also get or find a expression for n, the number of compound periods in terms of the other three quantities P, A and i. The expression is
  

  n =    log A P log(1+i)

  Understanding this requires familiarity with logarithms. Using it requires say a calculator with a log button. Again, why or how this last formula is obtained is left as an intellectual IOU.

You have seen the derivation of the first two of the above formulas from the compound interest formula. Explanation of the third is left as an intellectual debt. This chapter has shown the usefulness of algebra and shorthand notation in dealing with the compound interest formula. The further study of powers, roots and logarithms is left to another text.

Further Readings

1. Mathematics of Finance, 3rd Edition by P. Zima & R. Brown, McGraw-Hill Ryerson Ltd, IBSN: 0-07-549491-4,
2. The chapter Money Computations below.

More Chapter Sections: [ Up ] [ 14 The Formula ] [ 14. Direct Use - First Example ] [ 14. Direct Use, Second Example ] [ 14 Indirect Use - First Example I ] [ 14 Indirect Use - Second Example ] [ 14 Going Further ]

Postscript: Derivation of formula for n assuming a knowledge of logarithms.