a. You invest $12,000 today at 9 percent per year. How much will you have after 15 years? b. What is the current value of $100,000 after 10 years if the discount rate is 12 percent? c. You invest $2,000 a year for 20 years at 11 percent. How much will you have after 20 years?

Question

a. You invest [latex]\$ 12,000[/latex] today at 9 percent per year. How much will you have after 15 years?

b. What is the current value of [latex]\$ 100,000[/latex] after 10 years if the discount rate is 12 percent?

c. You invest [latex]\$ 2,000[/latex] a year for 20 years at 11 percent. How much will you have after 20 years?

Accepted Answer

a. This is the future value of a single amount.

[latex] \begin{array}{ll} \mathrm{FV} & =\mathrm{PV} imes \mathrm{FV}_{\mathrm{IF}}(\mathrm{n}=15, \mathrm{i}=9 \%) \quad ext { Appendix } \mathrm{A} \ \mathrm{FV} & =\$ 12,000 imes 3.642=\$ 43,704 \end{array} [/latex]

b. This is the present value of a single amount.

[latex] \begin{array}{l} \mathrm{PV}=\mathrm{FV} imes \mathrm{PV}_{\mathrm{IF}}(\mathrm{n}=10, \mathrm{i}=12 \%) \quad ext { Appendix } \mathrm{B} \ \mathrm{PV}=\$ 100,000 imes .322=\$ 32,200 \end{array} [/latex]

c. This is the future value of an annuity.

[latex] \begin{array}{l} \mathrm{FV}_{\mathrm{A}}=\mathrm{A} imes \mathrm{FV}_{\mathrm{IFA}} \quad(\mathrm{n}=20, \mathrm{i}=11 \%) \quad ext { Appendix } \mathrm{C} \ \mathrm{FV}_{\mathrm{A}}=\$ 2,000 imes 64.203=\$ 128,406 \end{array} [/latex]

Question 9.1: a. You invest $12,000 today at 9 percent per year. How much ...

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