Question

Stephanie Watson is 20 years old and plans to make the following investments beginning next year....

Stephanie Watson is 20 years old and plans to make the following investments beginning next year. She will invest $3,125 in each of the next three years and will then make investments of $3,650, $3,725, $3,875, and $4,000 over the following four years. If the investments are expected to earn 11.5 percent annually, how much will Stephanie have when she turns 30?

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Answer #1

Given

CF1 = 3125
CF2 = 3125
CF3 = 3125
CF4 = 3640
CF5 = 3725
CF6 = 3875
CF7 = 4000

Rate of return = r = 11.5% or 0.115

PV of the investments (at age 20) = CF1/(1+r) + CF2/(1+r)2 + CF3/(1+r)3 +.... + CF7/(1+r)7

= 3125/(1.0115) + 3125/(1.0115)2 + 3125/(1.0115)3 + 3640/(1.0115)4 + 3725/(1.0115)5 + 3875/(1.0115)6 + 4000/(1.0115)7  

= $23469.09

Value of investment after n = 10 years i.e when Stephanie turns 30 = FV = PV(1+r)10 = 23469.09*1.11510 = $69701.95

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