You are investing to achieve the following goals: A down payment for a cottage in the amount of $8000 in six years,$4000 for a trip to Europe in three years,and $150000 to supplement retirement income in 24 years.If you can earn 7 percent compounded monthly on your investments,how much should you be saving each month?

Question

Quizplus · Accepted Answer

To calculate the monthly savings needed to achieve each goal, we use the future value of an annuity formula: $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)$, where $FV$ is the future value, $P$ is the monthly payment, $r$ is the monthly interest rate, and $n$ is the total number of payments. Since the interest rate is compounded monthly, we divide the annual rate by 12. For each goal:1. **Cottage Down Payment ($8,000 in 6 years)**:   - $r = \frac{0.07}{12}$   - $n = 6 \times 12 = 72$   - Solving for $P$ gives the monthly amount needed for this goal.2. **Trip to Europe ($4,000 in 3 years)**:   - $r = \frac{0.07}{12}$   - $n = 3 \times 12 = 36$   - Solving for $P$ gives the monthly amount needed for this goal.3. **Retirement Supplement ($150,000 in 24 years)**:   - $r = \frac{0.07}{12}$   - $n = 24 \times 12 = 288$   - Solving for $P$ gives the monthly amount needed for this goal.After calculating $P$ for each goal, summing these amounts gives the total monthly savings required. The correct total, based on these calculations, is approximately $392, making option A the correct answer.

You Are Investing to Achieve the Following Goals: a Down