Future Value of an Annuity Find the future value of the following annuities. The

Question

Future Value of an Annuity

Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1; that is, they are ordinary annuities. Round your answers to the nearest cent. (Notes: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in many situations, to see how changes in input variables affect the output variable. Also, note that you can leave values in the TVM register, switch to Begin Mode, press FV, and find the FV of the annuity due.)

Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.

Explanation / Answer

a. N = 5 I = 12 PV = -500 PMT = 0 FV = ?
FV = $881.17
b. N = 10 I = 6 PV = -500 PMT = 0 FV = ?
FV = $895.42
c. N = 20 I = 3 PV = -500 PMT = 0 FV = ?
FV = $903.06
d. N = 60 I = 1 PV = -500 PMT = 0 FV = ?
FV = $908.35
e. N = 1825 I = 0.032877 PV = -500 PMT = 0 FV = ?
FV = $910.97
f. The FV's increase because the compounding periods increase, interest is earned on interest more frequently.

???

find the PV of $500 due in the future under each of these conditions

a. 12% nominal rate, semiannual compounding, discounted back 5 years
b. 12% nominal rate, quarterly compounded, discounted back 5 years
c. 12% nominal rate, monthly compounding, discounted back 1 year.
d. why do the differences in the PV's occur?

a. N = 10 I = 6 PMT = 0 FV = 500 PV = ?
PV = $279.20
b. N = 20 I = 3 PMT = 0 FV = 500 PV = ?
PV = $276.84
c. N = 12 I = 1 PMT = 0 FV = 500 PV = ?
PV = $443.72
d. The PV's for parts a and b decline as periods increase. This occurs with more frequent compounding, a smaller initial amount is required to get $500 after 5 years.

???

find the future values of the following ordinary annuities:

a. FV $400 paid each 6 months for 5 years at a nominal rate of 12%, compounded semiannually

b. FV if $200 paid each 3 months for 5 years at a nominal rate of 12%, compounding quarterly

c. these annuities receive the same amount in cash during the 5 year period and earn interest at the same nominal rate, yet the annuity in part b ends up larger than the one in part a. why does this occur?

a. N = 10 I = 6 PV = 0 PMT = -400 FV = ?
FV = $5272.32
b. a. N = 20 I = 3 PV = 0 PMT = -400 FV = ?
FV = $5374.07
c. The annuity in part b earns more because the money is on deposit for a longer period of time and so earns more interest. Also, because compounding is more frequent, more interest is earned on interest.

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