Algebra help, Income earned on an IRA investment help?

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 $13,o00 from her IRA to help fund her retirement. She has placed $50,000 of this IRA in a secure Treasury bond earning 5% yearly interest. If she earns a 7% rate of return on the rest of this IRA through an insurance annuity, what is the principal that is invested in the insurance annuity? 

Answer 1

Formulas:
I=Prt
P=I/rt
Yearly Income=Interest amount from Treasury Bond+Interest amount from Insurance Annuity

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

 

 

Treasury Bond:

P=50,000

r=5%=.05

t=1

I=50,000(.05)(1)=2,500

 

Insurance Annuity:

I=13,000-2,500=10,500

r=7%=.07

t=1

P=10,500/(.07)(1)=150,000

P=$150,000