10/23 More interest Compound interest formula A =.

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Presentation transcript:

10/23 More interest Compound interest formula A =

Important polynomial identity: For any number x <> 1, and any positive integer n 1 + x + x^2 + …. + x^n = (x^(n+1) – 1) /(x-1)

Use this identity to calculate annuities: Example: 50 dollars is deposited at the end of each month into An account paying 6% annually compounded monthly. How much will you have after 20 years?

Use this identity to derive the formula for annuities: Example: R dollars is deposited at the end of each period into An account paying a rate of i annually compounded monthly. How much will you have after n periods?

Present value of an annuity = (mortgage loan). Suppose that you agree to pay off a loan of P dollars in 20 equal installments of 1000 dollars at an interest Rate of 3 % per period. What is P?

Present value of an annuity: the formula