Question

Mario goes around collecting money from random blocks and pipes. His income stream from this endeavor is roughly continuous, earning him $50,000 per year. The money he earns can be invested at an interest rate of 9%, compounded continuously, and he believes he can keep this job up for another 5 years before returning to his regular career as a plumber.

Mr. Bowser offers Mario $200,000 right now to abandon his money-collection pursuit. Find an expression involving an integral that Mario could calculate the value of to figure out if he should take Mr. Bowser’s deal or not. You do not need to calculate the value of the integral.

Mario proposes to Princess Peach. She says she will marry Mario only if he can afford a $300,000 wedding in five years. Determine an integral whose value will determine whether Mario will indeed spend eternity with the girl of his dreams. You do not need to calculate the value of the integral.

Answer 1

1. Mario deposit the money from current year onwards the first $50000 for 5years and gradually years comes down upto 5th year.The amount will be $3379797,61

Amount	Years	Future value (Compounded)
50000	5	78,284.05{ 50000(1+0.09/12) for 5 years]
50000	4	71,570.27{ 50000(1+0.09/12) for 4 years}
50000	3	65,432.27{ 50000(1+0.09/12) for 3 years}
50000	2	59,820.68{ 50000(1+0.09/12) for 2 years}
50000	1	54,690.34{ 50000(1+0.09/12) for 1 years}
50000	0	50,000.00{ 50000(1+0.09/12)
Total	379,797.61

2. Bowser offer: Mario received an offer from Bowser amountingto $ 200000 now and he deposit the amount @9% and he will earn (200000*9%/60)=313136.21

As per Princess Peach Mario can afford $ 300000 wedding in five years,both cases meet the purpose but amount wise first option is better