Exercise 4 (Charity, Estate Planning, Bequest). An individual is retiring, and just noticed that they have more money than needed for retirement. They want to give all of their money away to their favorite charities now, except for an amount yo which will handle personal and family matters. This way, they can enjoy seeing their favorite charities do good work with their money while still alive. The amount yo must cover their retirement expenses of $100,000 per year for 30 years and a bequest of precisely $2,100,000 for their heirs at the end of that time. The amount yo will be in a retirement account that pays interest at an annual rate of r = 0.05 per year. 

In other words, yo is unknown, and the value of the account n years after retirement, for 1

Y_n = (1+r) · (y_n-1 - 100,000), 

and 

Y₃₀ = 2,100,000. 

The reason for the form of the difference equation is that the individual takes $100,000 out of the account to handle expenses for the whole year on January 1, and so only the remaining amount, Yn-1 - 100,000, earns interest for the year. Find yo. 

Answer rating: 100% (QA)

ANSWERS Yo 2100000 1 00530 Yo 2100000 10530 Yo 137924537 EXPANATIONS The difference equation is ... View the full answer