Al Darby wants to withdraw $20,000 (including principal) from an investment fund at the end of each year for five years. How should he compute his required initial investment at the beginning of the first year if the fund earns 10% compounded annually?
A) $20,000 times the future value of a 5-year, 10% ordinary annuity of 1.
B) $20,000 divided by the future value of a 5-year, 10% ordinary annuity of 1.
C) $20,000 times the present value of a 5-year, 10% ordinary annuity of 1.
D) $20,000 divided by the present value of a 5-year, 10% ordinary annuity of 1.

Question

Quizplus · Accepted Answer

To find the required initial investment, we need to calculate the present value of an annuity that pays $20,000 annually for five years at a 10% annual interest rate. This can be done using the formula for the present value of an ordinary annuity:
PV = PMT x [1 - (1+r)^-n] / r
where PV is the present value, PMT is the annuity payment, r is the interest rate, and n is the number of periods.
Substituting the values, we get:
PV = $20,000 x [1 - (1+0.10)^-5] / 0.10
PV = $20,000 x [1 - 0.6209] / 0.10
PV = $20,000 x 3.791
PV = $75,820.61
Therefore, the required initial investment at the beginning of the first year is $75,820.61, which is option C.

Al Darby Wants to Withdraw $20,000 (Including Principal) from an Investment