Question

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'd like a response to the following questions before we​ proceed:

a. What is the relationship between discounting and​ compounding?

b. What is the relationship between the​ present-value factor and the annuity​ present-value factor?

c. i. What will ​$5,800 invested for 28 years at 14 percent compounded annually grow​ to?     

ii. How many years will it take ​$390 to grow to ​$6,484.39 if it is invested at 13 percent compounded​ annually?     

iii. At what rate would ​$1 comma 900 have to be invested to grow to ​$4,826.67 in 16 ​years?

d. Calculate the future sum of ​$1,400​, given that it will be held in the bank for 24 years and earn 11 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 ​$1,600 per year for 28 years discounted back to the present at 13 ​percent? What would be the present value if it were an annuity​ due?

g. What is the future value of an ordinary annuity of ​$1,600 per year for 28 years compounded at 13 ​percent? What would be the future value if it were an annuity​ due?

h. You have just borrowed ​$240,000​, and you agree to pay it back over the next 10 years in 10 equal​ end-of-year payments plus 13 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 ​$1,800 per year discounted back to the present at 8 ​percent? j

. What is the present value of an annuity of ​$1,400 per year for 10​ years, with the first payment occurring at the end of year 10​ (that is, ten ​$1,400 payments occurring at the end of year 10 through year​ 19), given a discount rate of 7 ​percent?

k. Given a discount rate of 18 ​percent, what is the present value of a perpetuity of ​$1,300 per year if the first payment does not begin until the end of year​ 10?

Answer 1

a. What is the relationship between discounting and​compounding?
Discounting is the reverse of compounding. Discounting converts future value to present value. Compounding converts present value to future value

b. What is the relationship between the​ present-value factor and the annuity​ present-value factor?
Present value factor=1/(1+rate)^n
Present value annuity factor=1/rate*(1-1/(1+rate)^n)=1/rate*(1-Present Value Factor)

c. i. What will ​$5,800 invested for 28 years at 14 percent compounded annually grow​ to?
=5800*1.14^28
=$2,27,386.057

ii. How many years will it take ​$390 to grow to ​$6,484.39 if it is invested at 13 percent compounded​ annually?
=log(6484.39/390)/log(1+13%)
=23.00001

iii. At what rate would ​$1 comma 900 have to be invested to grow to ​$4,826.67 in 16 ​years?
=(4826.67/1900)^(1/16)-1
=6.00000247%

d. Calculate the future sum of ​$1,400​, given that it will be held in the bank for 24 years and earn 11 percent compounded semiannually.
=1400*(1+11%/2)^(2*24)
=$18,291.364

P.S.: I am not allowed to answer more than 4 questions