mathmodeling
posted by fazilah .
Person A opens an IRA at age 25, contributes $2000 per year for 10 years, but makes no additional contributions
thereafter. Person B waits until age 35 to open an IRA and contributes $2000 per years for 30 years. There is
no initial investment in either case.
a) Assuming an interest rate of 8%, what is the balance in each IRA at age 65?

person A
amount = 2000(1.08^10  1)/.08 * 1.08^30 = 291 546.62
person B
amount = 2000(1.08^30  1)/.08 = 226 566.42 
Reiny is actually wrong, this question is old but, for anyone looking for this answer:
Use the general form:
S(t)=S0e^(rt) + (k/r)(e^(rt)1)
S(t) is the money at any point
S0 is the initial investment
k is what is invested per year
r is the return rate (make sure to convert to a decimal)
t is the time in years
Person A)
No initial investment, so the money they invested over the 10 years is
s(10)= 0 + (2000/0.08)*(e^(10*0.08)1) = 30638.52
This money sits in there gaining return thereafter. Use it as s0 for the next 30 years (they are no longer making yearly investments) to see how much money they will have at 65:
s(30) = 30638.52*e^(0.08*30)+ 0 = $337,733.85
Person B)
No initial investment, so
s(30) = 0 + (2000/0.08)*(e^(0.08*30)1) = $250,579.41
:)
Respond to this Question
Similar Questions

Finance
A 46yearold man deposits a total of $2000 per period in an IRA until age 65. How much money will be in the account if the interest rate is 10% compounded semiannually with payments made at the end of each semiannual period? 
mathematical modeling
Person A opens an IRA at age 25, contributes $2000 per year for 10 years, but makes no additional contributes thereafter. Person B waits untill age 35 to open an IRA and contributes $2000 per year for 30 years. There is no initial … 
math modeling
Person A opens an IRA at age 25, contributes $2000 per year for 10 years, but makes no additional contributions thereafter. Person B waits until age 35 to open an IRA and contributes $2000 per years for 30 years. There is no initial … 
math
Michael invested $1600 per halfyear in an IRA each halfyear for 9 years earning 9% compounded semiannually. At the end of 9 years he ceased the IRA payments, but continued to invest his accumulated amount at 10% compounded yearly … 
Investments
At the end of each year a selfemployed person deposits $1,500 in a retirement account that earns 10 percent annually. a) How much will be in the account when the individual retired at the age of 65 if the contribution start when the … 
finance
A selfemployed person deposits $3,000 annually in a retirement account (called a Keogh account) that earns 8 percent. a. How much will be in the account when the individual retires at the age of 65 if the savings program starts when … 
Math
1. You need $200,000 to retire in 10 years. You can invest monthly amounts at 5% APR at work. How much should you contribute each month? 
Finance
Assume that you are 23 years old and that you place $3,000 yearend deposits each year into a stock index fund that earns an average of 9% per year for the next 17 years. 1. How much money will be in the account at the end of 17 years? 
everest online
2. At the end of each year a selfemployed person deposits $1,500 in a retirement account that earns 10 percent annually. a) How much will be in the accountant when the individual retires at the age of 65 if the contributions start … 
Math
Suppose that Ramos contributes $6000/year into a traditional IRA earning interest at the rate of 2%/year compounded annually, every year after 35 until his retirement age at age 65. At the same time, his wife Vanessa deposits $4900/year …