# mathmodeling

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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?

• mathmodeling -

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

• mathmodeling -

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

:)

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