# Calculate Future Value - DOC

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```					Calculate the future value of the following:
\$5,000 compounded annually at 6% for 5 years

FV=5000*(1.06^5) =\$6,691.13

\$5,000 compounded semiannually at 6% for 5 years

FV=5000*(1.03^10) =\$6,719.58

\$5,000 compounded quarterly at 6% for 5 years

FV=5000*(1.015^20) =\$6,734.28

\$5,000 compounded annually at 6% for 6 years

FV=5000*(1.06^6) = \$7,092.60

What conclusions can be drawn about the frequency of compounding interest?

As the frequency of compounding increases future value increases.

What conclusions can be drawn about the length of time an amount is compounding?

As the length of time an amount is compounding increases future value increases.

Calculate the present value of the following:

\$7,000 in 5 years at an annual discount rate of 6%

PV= 7000/(1.06^5) = \$5,230.81

\$7,000 in 5 years at a semiannual discount rate of 6%

PV= 7000/(1.03^10) = \$5,208.66

\$7,000 in 5 years at a quarterly discount rate of 6%

PV= 7000/(1.015^20)= \$5,197.29
\$7,000 in 6 years at an annual discount rate of 6%

PV= 7000/(1.06^6)= \$4,934.72

What conclusions can be drawn about the frequency of the discounting interval?

As the frequency of the discounting interval increases the present value decrease.

What conclusions can be drawn about the length of time until the receipt of that value?

As the length of time until the receipt of that value increases the present value
decrease.

Assume you have a choice between two annuity contracts.
Contract A pays \$5,000 per year for 5 years starting one year from today.

PV = 5000*PVIF Ordinary Annuity(6%, 5 periods) =5000*4.21236 =\$21061.80

Contract B pays \$5,000 per year for 5 years starting today.

PV = 5000*PVIF Annuity Due(6%, 5 periods) =5000*4.46511= \$22,325.55

The discount rate for each is 6%.
Which annuity contract would you choose for your retirement? Why?
We would choose contract B since it has higher present value.

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