In the compound interest example on P.344. Calculate S20 and T240. Which is the better investment after 20 years? Hence,S40 = (1.11)"(10 090.090 909. ..)(9 090.909 090...)= (65.000 867...)(10 090.090 909...)(9 090.909 090. ..)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 andTn+1 – T,+ interest on T,+$100-= T,+(1/12) of 10% of T„+$100= T„[1+0.1/12]+$100.%3D100In this RE, a = 12.1/12,c = 100, so1 --12000 and-0.1/12aT, = (12.1/12)"[100+12000] – 12000.Hence, after 40 × 12 months,T480 = (12.1/12)4" (12100)= (1.008 333...)+8° (12100) - (12000)= (53.700 663...)(12100)= 649 778.023 4...e $637 778.- (12000)480- (12000)- (12000)Therefore, Plan A has a slightly larger value after 40 years. Example 8.2.3: Compound InterestSuppose 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% simpleinterest, and you add $1,000. In Plan B, you start with $100, and each month, youare paid one-twelfth of 10% simple (annual) interest, and you add $100. Which planwill be larger after 40 years?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// Can we apply a recurrence equation?Sn+1 = Sn +interest on S,+ $1000= S„ +11% of S,= S„(1+0.11)+$1000+ $1000.1000In this RE, a = 1.11, c = 1000, so1and- a-0.1110001000Sn = (1.11)" | 1000-0.11-0.1111101000(1.11)"[+0.11]+0.11

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

Pfin (with Mindtap, 1 Term Printed Access Card) (mindtap Course List)

7th Edition

ISBN:9780357033609

Author:Randall Billingsley, Lawrence J. Gitman, Michael D. Joehnk

Publisher:Randall Billingsley, Lawrence J. Gitman, Michael D. Joehnk

Chapter4: Managing Your Cash And Savings

Section: Chapter Questions

Problem 7FPE: Calculating interest earned and future value of savings account. If you put 6,000 in a savings...

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