(a) A 25 year old college graduate opens an IRA account with $1200 at the end of the first year and continues to deposit $1200 into the account each year until turning age 65 never making any withdrawals Assume for the sake of a simplified model that each deposit is made continuously (Le , a little bit cach day spread over the entire year) and earns a continuous growth rate of return of 7 per year (i) Write down a differential equation to describe the rate of change of the quantity of money Q(t) in the college graduate's IRA account after 1 year (ii) How much money will be in the account when the college graduate turns age 65, i e after 40 years Explain your method of calculation (You may use either Euler's Method or an analytical formula ) (b) The college student's parents have a retirement fund of $800,000 saved in an account that cams a continuous growth rate of 4 per year They want to withdraw a constant amount of W dollars each year For simplicity, assume that the withdrawal is made continuously throughout the year (i) Write down a differential equation to describe the rate of change of the quantity of money R(1) in the parents' retirement fund after years (ii) Find the value W that the parents could withdraw each year without any change in the value of RO) (iii) Suppose the parents withdraw $45,000 each year How long will their retirement fund last Explain your method of calculation (You may use either Euler's Method or an analytical formula solution )

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Posted on Jun 15, 2022

(a) A 25-year-old college graduate opens an IRA account with $1200 at the end of the first year and continues to deposit $1200 into the account each year until turning age 65. never making any withdrawals. Assume for the sake of a simplified model that each deposit is made continuously (Le., a little bit cach day spread over the entire year) and earns a continuous growth rate of return of 7% per year
(i) Write down a differential equation to describe the rate of change of the quantity of money Q(t) in the college graduate's IRA account after 1 year.
(ii) How much money will be in the account when the college graduate turns age 65, i.e. after 40 years? Explain your method of calculation. (You may use either Euler's Method or an analytical formula.)
(b) The college student's parents have a retirement fund of $800,000 saved in an account that cams a continuous growth rate of 4% per year. They want to withdraw a constant amount of W dollars each year. For simplicity, assume that the withdrawal is made continuously throughout the year.
(i) Write down a differential equation to describe the rate of change of the quantity of money R(1) in the parents' retirement fund after / years.
(ii) Find the value W that the parents could withdraw each year without any change in the value of RO).
(iii) Suppose the parents withdraw $45,000 each year. How long will their retirement fund last? Explain your method of calculation. (You may use either Euler's Method or an analytical formula solution.)