Question

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?

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*1.115^{10} =
$69701.95

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