Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
In the compound interest example on P.344. Calculate S20 and T240. Which is the better investment after 20 years?

In the compound interest example on P.344. Calculate S20 and T240. Which is the better investment after 20 years?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 54E
See similar textbooks
icon
Related questions
Question
100%

In the compound interest example on P.344. Calculate S20 and T240. Which is the better investment after 20 years?

Example 8.2.3: Compound Interest Suppose you are offered two retirement savings plans. In Plan A, you start with $1,000, and each year (on the anniversary of the plan), you are paid 11% simple interest, and you add $1,000. In Plan B, you start with $100, and each month, you are paid one-twelfth of 10% simple (annual) interest, and you add $100. Which plan will be larger after 40 years? // Can we apply a recurrence equation? Consider Plan A and let S, denote the number of dollars in the plan after (exactly) n years of operation. Then So $1,000 and Sn+1 = Sn + interest on S,+$1000 = S, +11% of S, = S,(1+0.11) + $1000 + $1000. 1000 In this RE, a = 1.11, c= 1000, so and 1 - a -0.11 1000 S, = (1.11)" | 1000 1000 + -0.11 -0.11 1110 1000 = (1.11)" +0.11 +0.11
Transcribed Image Text:Example 8.2.3: Compound Interest Suppose you are offered two retirement savings plans. In Plan A, you start with $1,000, and each year (on the anniversary of the plan), you are paid 11% simple interest, and you add $1,000. In Plan B, you start with $100, and each month, you are paid one-twelfth of 10% simple (annual) interest, and you add $100. Which plan will be larger after 40 years? // Can we apply a recurrence equation? Consider Plan A and let S, denote the number of dollars in the plan after (exactly) n years of operation. Then So $1,000 and Sn+1 = Sn + interest on S,+$1000 = S, +11% of S, = S,(1+0.11) + $1000 + $1000. 1000 In this RE, a = 1.11, c= 1000, so and 1 - a -0.11 1000 S, = (1.11)" | 1000 1000 + -0.11 -0.11 1110 1000 = (1.11)" +0.11 +0.11
8.2 Solving First-Order Linear Recurrence Equations 345 Hence, S40 = (1.11)"(10 090.090 909...) -(9 090.909 090. ..) - (9 090.909 090...) (65.000 867...)(10 090.090 909...) 655 917.842. .. - (9 090.909 090. ..) e $646 826. // Can that be right? You put in $40,000 and take out > $600,000 in interest. Now consider Plan B and let T, denote the number of dollars in the plan after (exactly) n months of operation. Then To $100 and Tn+1 = Tn+interest on T, +$100 = T,+(1/12) of 10% of T, + $100 = T„[1+0.1/12] +$100. 100 In this RE, a = 12.1/12, = 100, so -12000 and -0.1/12 T, = (12.1/12)"[100+ 12000] – 12000. 1 - a Hence, after 40 × 12 months, (12.1/12)*8° (12100) : (1.008 333...)*8" (12100) - (12000) (53.700 663...)(12100) 649 778.023 4... 480 T480 - (12000) 480 – (12000) - (12000) %3| e $637 778. Therefore, Plan A has a slightly larger value after 40 years.
Transcribed Image Text:8.2 Solving First-Order Linear Recurrence Equations 345 Hence, S40 = (1.11)"(10 090.090 909...) -(9 090.909 090. ..) - (9 090.909 090...) (65.000 867...)(10 090.090 909...) 655 917.842. .. - (9 090.909 090. ..) e $646 826. // Can that be right? You put in $40,000 and take out > $600,000 in interest. Now consider Plan B and let T, denote the number of dollars in the plan after (exactly) n months of operation. Then To $100 and Tn+1 = Tn+interest on T, +$100 = T,+(1/12) of 10% of T, + $100 = T„[1+0.1/12] +$100. 100 In this RE, a = 12.1/12, = 100, so -12000 and -0.1/12 T, = (12.1/12)"[100+ 12000] – 12000. 1 - a Hence, after 40 × 12 months, (12.1/12)*8° (12100) : (1.008 333...)*8" (12100) - (12000) (53.700 663...)(12100) 649 778.023 4... 480 T480 - (12000) 480 – (12000) - (12000) %3| e $637 778. Therefore, Plan A has a slightly larger value after 40 years.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS