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# Calculating the present value of different annuities

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Find:
- the present value of \$300,000 annuity at 6% for 20 years
- the present value of \$500,000 deferred annuity at 6% for 20 (21-40) years
- the present value of 50,000 annuity at 6% for 40 years
- the present value of 75 million paid at the end of 40 years
- the present value of 300,000 annuity at 11% for 20 years
- the present value deferred annuity at 6% for 20 (21-40) years what is the value at the end of 40 years

#### Solution Preview

a. Present Value of \$300,000 annuity at 6% for 20 years
Annuity amount=R=\$300,000
Discount rate=i=6%
Number of periods=n=20
PV of an ordinary annuity is given by
PV=R/i*(1-1/(1+i)^n)=300000/6%*(1-1/(1+6%)^20)= \$3,440,976.37

b. Present Value of\$500,000 deferred annuity at 6% for 20 (21-40) years
Annuity amount=R=\$500,000
Discount rate=i=6%
Number of periods=n=20
PV of an ...

#### Solution Summary

Concepts of annuities play an important role in finance. Solutions to given problem set depict the methodology to calculate the present value of annuity and deferred annuity as the case may be. Solutions are derived with the help of suitable annuity formulas.

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