Suppose you invest $1,000 at 8% simple interest (compounded at the end of each y

Question

Suppose you invest $1,000 at 8% simple interest (compounded at the end of each year). Let 'An' denote the amount of money that you have at the end of n years. Since you are starting with $1,000, it is reasonable to let A0=1,000.

a. How much money will you have at the end of 5 years (i.e. Calculate A5)?

b. Describe the sequence A0, A1, A2,....,An,.... with a recursive formula.

c. Describe the sequence A0, A1, A2,....,An,.... with an explicit formula.

d. Use the explicit formula that you found in part c (and use your calculator) to compute A12.

Reproduced from page FIGURE 1.7.3 Suppose you invest $1,000 at 8% simple interest (compounded at the e year). Let An denote the amount of money that you have at the end of Since you are starting with $1,000, it is reasonable to let A0 1,000. a. How much money will you have at the end of 5 years (i.e., calcula b. Describe the sequence Ao.A.A. with a recursive formula. c. Describe the sequence Ao,A1,A2,..An.. . with an explicit formula d. Use the explicit formula that you found in part c (and use your calculator)to e end of each ed at ná of n years. e at the end of n ate As)? compute A12 d of a trianole form a finite geometric sequence

Explanation / Answer

(a)
A5 = 1000*(1+0.08)^5 = $1469.33

(b)

An = An-1(1+0.08) = 1.08An-1

(c)

An = 1000(1.08)^n

(d)

A12 = 1000(1.08)^12 = $2518.17

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