a. How much must Katie Wilson set aside each year to accumulate $\$ 80,000$ after 15 years? The interest rate is 10 percent.

b. How much must Josh Thompson repay each year for five years to pay off a $\$ 20,000$ loan that he just took out? The interest rate is 8 percent.

Question

a. How much must Katie Wilson set aside each year to accumulate [latex]\$ 80,000[/latex] after 15 years? The interest rate is 10 percent.

b. How much must Josh Thompson repay each year for five years to pay off a [latex]\$ 20,000[/latex] loan that he just took out? The interest rate is 8 percent.

Accepted Answer

a. This calls for solving for an annuity to equal a future value.

[latex] \begin{array}{l} \mathrm{A}=\frac{\mathrm{FV}_{\mathrm{A}}}{\mathrm{FV}_{\mathrm{IFA}}} \quad(\mathrm{n}=15, \mathrm{i}=10 \%) \quad ext { Appendix } \mathrm{C} \ \mathrm{A}=\frac{\$ 80,000}{31.772}=\$ 2,517.94 \end{array} [/latex]

b. The [latex]\$ 20,000[/latex] he is borrowing represents an amount he owes today. He will make future annual payments to pay off this current (present) obligation.

This calls for solving for an annuity equal to a present value.

[latex] \begin{array}{l} \mathrm{A}=\frac{\mathrm{PV}_{\mathrm{A}}}{\mathrm{PV}_{\mathrm{IFA}}} \quad(\mathrm{n}=5, \mathrm{i}=8 \%) \quad ext { Appendix } \mathrm{D} \ \mathrm{A}=\frac{\$ 20,000}{3.993}=\$ 5,008.77 \end{array} [/latex]

Question 9.2: a. How much must Katie Wilson set aside each year to accumul...

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