Algebra help, Income earned on an IRA investment

Question

I need some help on setting up this problem, and how to find the formula to get the correct answer..

Here it is: A retiree needs a yearly income of $10,200 from his $150,000 IRA to help fund his retirement. HE has placed $60,000 of this account in a secure Treasury bond earning 5% yearly interest. What rate of return must he earn on the rest of the investment to reach his $10,200 income goal?

Answer 1

Formulas:
I=Prt
r=I/Pt
Yearly Income=Interest amount from Treasury Bond+Interest amount from the rest of the investment

IRA Principal=Treasury Bond Principal+Rest of the Investment Principal

I=Interest amount
P=Principal amount
r=interest rate
t=time period in years

 

 

Treasury Bond:

P=60,000

r=5%=.05

t=1

I=60,000(.05)(1)=3,000

 

Rest of the Investment:

I=10,200-3,000=7,200

P=IRA Principal-Treasury Bond Principal=150,000-60,000=90,000

t=1

r=7,200/(90,000)(1)=.08

r=8%