MHB Solve the $5000 Annuity Investment Today

[Suraphel]

Dear All,
Kindly help me by solving the following question, it gives me hard time to solve especially the word "commencing". Thank in advance.

How much would need to be invested today at 6% per annum to provide an annuity of $5000 per ten years commencing in 5 years.

 

[HallsofIvy]

"$5000 per 10 years"? Do you mean "$5000 per year for 10 years"?

"Commencing in five years" means that the initial principle draws interest for 5 years before any payout starts. If we call the principle "P" then after 5 years at 6% simple interest (you don't mention compounding) you will have P+ 5(0.06P)= P+ 0.30P= 1.3P.

The next year you will gain 0.6(1.3P) in interest but pay out $5000 so will have 0.06(1.3P)- 5000= [FONT=Verdana,Arial,Tahoma,Calibri,Geneva,sans-serif]0.078P- 5000.

The third year you will gain 0.6(0.078P- 5000) but pay out $5000 so will have 0.06(0.078P- 5000)- 5000= [FONT=Verdana,Arial,Tahoma,Calibri,Geneva,sans-serif]0.00468P- 5300.

Continue in that way through the 10 year, set that formula in P equal to 0, and solve for P.