Question

You invested your summer earnings into and annuity from which you can draw expenses while you are at university. If you need to withdraw $1200 each month for 9 months of university, how much do you need to invest into an account, earning 6% per year, compounded semi-annually, in order to cover your expenses?

Answer 1

Answer:

10538.07

Step-by-step explanation:

find the effective semiannual rate: .06/2= .03

conver this into an effective monthly rate

$(1.03)^2=(1+i)^{12}\\(1.03)^{1/6}-1=i\\i=.0049386220312$

this is our montlhy effective rate. use this to calculate teh present value of 9 1200 dollars payments

$1200(\frac{1-(1+.0049386220312)^{-9}}{.0049386220312})=10538.0729871$

which rounds to 10538.07