Question

Alysha plans to invest $3000 in an equity fund every year end beginning this year. The...

Alysha plans to invest $3000 in an equity fund every year end beginning this year. The expected annual return on the fund is 15 percent. She plans to invest for 18 years. What is the present value of Alysha’s investments?

A. $18384

B. $21141

C. $18595

D. $18141

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Answer #1

Investment is made at end of each year.So it is a series of ordinary annuity for 18 years.

Ordinary annuity is defined as series of consecutive payment for a fixed period.

Present value of annuity = PMT /R% ( 1- (1+R%)^-N)

Where, PMT is regular payment
R% is rate of return
and N is time period.
Here,
Each year investment (PMT) = $ 3000
Expected Annual return (R%) = 15%
Time Period (N) = 18 Years
Present value of Investment = $ 3000/ 15% * ( 1- ( 1+15%)^-18)
Present value of Investment = $ 20,000 * ( 1- ( 1.15)^-18)
Present value of Investment = $ 20,000 * ( 1- 0.080805)
Present value of Investment = $ 18383.90
Answer : A. 18384
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