Posted by fazilah on Thursday, August 18, 2011 at 4:33am.
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 - Reiny, Thursday, August 18, 2011 at 7:44am
amount = 2000(1.08^10 - 1)/.08 * 1.08^30 = 291 546.62
amount = 2000(1.08^30 - 1)/.08 = 226 566.42
mathmodeling - Marni, Tuesday, December 13, 2016 at 5:32pm
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
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
No initial investment, so
s(30) = 0 + (2000/0.08)*(e^(0.08*30)-1) = $250,579.41
Answer This Question
More Related Questions
- math modeling - Person A opens an IRA at age 25, contributes $2000 per year for ...
- mathematical modeling - Person A opens an IRA at age 25, contributes $2000 per ...
- math - Michael invested $1600 per half-year in an IRA each half-year for 9 years...
- Math - Suppose that Ramos contributes $6000/year into a traditional IRA earning ...
- everest online - 2. At the end of each year a self-employed person deposits $1,...
- Finance - Assume that you are 23 years old and that you place $3,000 year-end ...
- Math - 1. You need $200,000 to retire in 10 years. You can invest monthly ...
- Finance - A 46-year-old man deposits a total of $2000 per period in an IRA until...
- Investments - At the end of each year a self-employed person deposits $1,500 in ...
- finance - A self-employed person deposits $3,000 annually in a retirement ...