### What is the relationship between discounting and compounding

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Question: a. What is the relationship between discounting and compounding?

b. Distinguish between the present value factor and the annuity present value factor?

c-1. What will \$ 6,700 invested for 28 years at 11 percent compounded annually grow to?

c-2. How many years will it take \$ 540 to grow to \$ 11,515.44 if it is invested at 12 percent compounded annually?

c-3. At what rate would \$ 1,700 have to be invested to grow to \$20,692.71 in 29 years?

d. Calculate the future sum of \$1,200 , given that it will be held in the bank for 5 years and earn 14 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 6 years discounted back to the present at 11 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 6 years compounded at 11 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 20 years in 20 equal end-of-year payments plus 11 percent compound interest on the unpaid balance. What will be the size of these payments?

i. What is the present value of a \$1,200 perpetuity discounted back to the present at 14 percent?

j. What is the present value of a \$ 1,600 annuity 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 16 percent?

k.Given a discount rate of 8 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?

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