For your job as the business reporter for a local newspaper, you are given the task of putting together a series of articles that explain the power of the time value of money to your readers. Your editor would like you to address several specific questions in addition to demonstrating for the readership the use of time value of money techniques by applying them to several problems. What would be your response to the following memorandum from your editor?

To: Business Reporter

From: Perry White, Editor, Daily Planet

Re: Upcoming Series on the Importance and Power of the Time Value of Money

In your upcoming series on the time value of money, I would like to make sure you cover several specific points. In addition, before you begin this assignment, I want to make sure we are all reading from the same script, as accuracy has always been the cornerstone of the Daily Planet. In this regard, I$\text{'}$d like a response to the following questions before we proceed:

c$.$ i$.$ What will $$6,400$ invested for $27$ years at $14$ percent compounded annually grow to$?$

ii$.$ How many years will it take $$580$ to grow to $$3,103\mathrm{.}15$ if it is invested at $15$ percent compounded annually?

iii. At what rate would $$1,100$ have to be invested to grow to $$2,486\mathrm{.}99$ in $14$ years?

d$.$ Calculate the future sum of $$1,500,$ given that it will be held in the bank for $29$ years and earn $8$ percent compounded semiannually.

e$.$ What is an annuity due? How does this differ from an ordinary annuity?

f$.$ What is the present value of an ordinary annuity of $$1,100$ per year for $23$ years discounted back to the present at $15$ percent? What would be the present value if it were an annuity due?

g$.$ What is the future value of an ordinary annuity of $$1,100$ per year for $23$ years compounded at $15$ percent? What would be the future value if it were an annuity due?

h$.$ You have just borrowed $$160,000,$ and you agree to pay it back over the next $25$ years in $25$ equal end$-$of$-$year payments plus $9$ percent compound interest on the unpaid balance. What will be the size of these payments?

i$.$ What is the present value of a perpetuity of $$1,300$ per year discounted back to the present at $12$ percent?

j$.$ What is the present value of an annuity of $$1,600$ per year for $10$ years, with the first payment occurring at the end of year $10($that is$,$ ten $$1,600$ payments occurring at the end of year $10$ through year $19),$ given a discount rate of $7$ percent?

k$.$ Given a discount rate of $13$ percent, what is the present value of a perpetuity of $$1,700$ per year if the first payment does not begin until the end of year $10?$