Share
Explore BrainMass

# Time value of money, FV, PV, annuity, amortize, coupounding

3- Time value of money -
It is now January 1, 2006, and you will need \$1,000 on January 1, 2010, in 4 years. Your bank compounds interest at an 8 percent annual rate.

a. How much must you deposit today to have a balance of \$1,000 on January 1, 2010?

b. If you want to make 4 equal payments on each January 1 from 2007 through 2010 to accumulate the \$1,000, how large must each payment be?
( Note that the payments begin a year from today.)

c. If your father were to offer either to make the payments calculated in part b (\$221.92) or to give you \$750 on January 1, 2007 ( a year from today), which would you choose? Explain.

d. If you have only \$750 on January 1, 2007, what interest rate, compounded annually for 3 years, must you earn to have \$1,000 on January 1, 2010?

e. Suppose you can deposit only \$200 each January 1 from 2007 through 2010 (4 years). What interest rate, with annual compounding, must you earn to end up with \$1,000 on January 1, 2010?

f. Your father offers to give you \$400 on January 1, 2007. You will then make 6 additional equal payments each 6 months from July 2007 through January 2010. If your bank pays 8 percent, compounded semiannually, how large must each payment be for you to end up with \$1,000 on January 1, 2010?

g. What is the EAR, or EFF%, earned on the bank account in part f? What is the APR earned on the account?

16- Present value of a perpetuity-
What is the present value of a \$100 perpetuity if the interest rate is 7 percent? If interest rates doubled to 14 percent, what would its present value be?

#### Solution Preview

Question:
Time Value of Money

3- Time value of money -
It is now January 1, 2006, and you will need \$ 1,000 on January 1, 2010, in 4 years. Your bank compounds interest at an 8 percent annual rate.

a. How much must you deposit today to have a balance of \$ 1,000 on January 1, 2010?

b. If you want to make 4 equal payments on each January 1 from 2007 through 2010 to accumulate the \$ 1,000, how large must each payment be?
( Note that the payments begin a year from today.)

c. If your father were to offer either to make the payments calculated in part b (\$ 221.92) or to give you \$ 750 on January 1, 2007 ( a year from today), which would you choose? Explain.

d. If you have only \$ 750 on January 1, 2007, what interest rate, compounded annually for 3 years, must you earn to have \$ 1,000 on January 1, 2010?

e. Suppose you can deposit only \$ 200 each January 1 from 2007 through 2010 ( 4 years). What interest rate, with annual compounding, must you earn to end up with \$ 1,000 on January 1, 2010?

f. Your father offers to give you \$ 400 on January 1, 2007. You will then make 6 additional equal payments each 6 months from July 2007 through January 2010. If your ...