College Algebra-.docx

# College Algebra-.docx - r 1 1 n P 1 C t)= r n n 1 1 r n nt...

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C ( t )= P ( 1 + r n ) n [ 1 ( 1 + r n ) nt ] 1 ( 1 + r n ) n 1. How much will you have accumulated over a period of 35 years if, in an IRA which has a 8% interest rate compounded monthly, you annually invest: a. \$1 Data P=\$1 r=0.08 t=35 years n=1 C ( t ) = 1 ( 1 + 0.08 1 ) 1 [ 1 ( 1 + 0.08 1 ) 1 35 ] 1 ( 1 + 0.08 1 ) 1 = \$ 186.102 b. \$1,000 Data P=\$1,000 r=0.08 t=35 years n=1 C ( t ) = 1,000 ( 1 + 0.08 1 ) 1 [ 1 ( 1 + 0.08 1 ) 1 35 ] 1 ( 1 + 0.08 1 ) 1 = \$ 186102.15 c. \$4,500 Data P=\$4,500 r=0.08 t=35 years n=1 C ( t ) = 4,500 ( 1 + 0.08 1 ) 1 [ 1 ( 1 + 0.08 1 ) 1 35 ] 1 ( 1 + 0.08 1 ) 1 = \$ 837459.67 d. Part (a) is called the effective yield of an account. How could Part (a) be used to determine Parts (b) and (c)? (Your answer should be in complete sentences free of grammar, spelling, and punctuation mistakes.)

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Part b) can be obtained multiplying the results of Part a) by 1000, and Part c) can be obtained multiplying this result by 4,500. 2. How much will you have accumulated, if you annually invest \$2500 into an IRA at 11% interest compounded quarterly for: a. 10 years Data P=\$2,500 r=0.11 t=10 years n=4 C ( t ) = 2,500 ( 1 + 0.11 4 ) 4 [ 1 ( 1 + 0.11 4 ) 4 10 ] 1 ( 1 + 0.11 4 ) 4 = \$ 26570.20 b. 20 years Data P=\$2,500 r=0.11 t=20 years n=4 C ( t ) = 2,500 ( 1 + 0.11 4 ) 4 [ 1 ( 1 + 0.11 4 ) 4 20 ] 1 ( 1 + 0.11 4 ) 4 = \$ 56225.47 c. 30 years Data P=\$2,500 r=0.11 t=30 years n=4 C ( t ) = 2,500 ( 1 + 0.11 4 ) 4 [ 1 ( 1 + 0.11 4 ) 4 30 ] 1 ( 1 + 0.11 4 ) 4 = \$ 89323.99 d. How long will it take to earn your first million dollars? e.
1,000,000 = 2,500 ( 1 + 0.11 4 ) 4 [ 1 ( 1 + 0.11 4 ) 4 t ] 1 ( 1 + 0.11 4 ) 4

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1,000,000 [ 1 ( 1 + 0.11 4 ) 4 ] 2,500 ( 1 + 0.11 4 ) 4 = [ 1 ( 1 + 0.11 4 ) 4 t ] 1,000,000 [ 1 ( 1 + 0.11 4 ) 4 ] 2,500 ( 1 + 0.11 4 ) 4 = 1 ( 1 + 0.11 4 ) 4 t t 34 years plus 5 months 3. Now you will plan for your retirement. To do this we need to first determine a couple of values.
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