Linda Scales is now employed as the managing editor of a well-known business journal. Although she thoroughly enjoys her job and the people she works with, what she would really like to do is open a bookstore of her own. She would like to open her store in about eight years and figures she’ll need about $ 50,000 in capital to do so. Given that she thinks she can make about 10 percent on her money, use Worksheet 11.1 to answer the following questions. a.
How much would Linda have to invest today, in one lump sum, to end up with $ 50,000 in eight years?
b. If she’s starting from scratch, how much would she have to put away annually to accumulate the needed capital in eight years?
c. If she already has $ 10,000 socked away, how much would she have to put away annually to accumulate the required capital in eight years?
d. Given that Linda has an idea of how much she needs to save, briefly explain how she could use an investment plan to help reach her objective.
been having a hard time.
a. To calculate how much Linda would have to invest today, in one lump sum, to end up with $50,000 in eight years, we can use the future value formula:
FV = PV * (1 + r)^(n)
Where:
FV = Future Value ($50,000)
PV = Present Value (What Linda needs to invest today)
r = Interest rate (10% or 0.10)
n = Number of periods (8 years)
Plugging in the values, the formula becomes:
$50,000 = PV * (1 + 0.10)^8
We can rearrange the formula to solve for PV:
PV = $50,000 / (1 + 0.10)^8
Using a calculator, PV should be around $27,017.57.
Therefore, Linda would need to invest approximately $27,017.57 today in a lump sum to end up with $50,000 in eight years.
b. If Linda is starting from scratch, she would need to calculate the annual investment required to accumulate the needed capital in eight years. We can use the present value of an ordinary annuity formula:
PV = PMT * [(1 - (1 + r)^-n) / r]
Where:
PV = Present Value (Starting from $0)
PMT = Payment (Annual investment required)
r = Interest rate (10% or 0.10)
n = Number of periods (8 years)
Plugging in the values, the formula becomes:
$0 = PMT * [(1 - (1 + 0.10)^-8) / 0.10]
Rearranging the formula to solve for PMT:
PMT = $50,000 / [(1 - (1 + 0.10)^-8) / 0.10]
Using a calculator, PMT should be around $4,607.73.
Therefore, Linda would need to put away approximately $4,607.73 annually to accumulate the needed capital in eight years.
c. If Linda already has $10,000 socked away, she would need to calculate the additional annual investment required to accumulate the required capital in eight years. The approach is similar to part b, except that now we subtract the $10,000 she already has from the necessary capital:
Necessary Capital = $50,000 - $10,000 = $40,000
Using the same present value of an ordinary annuity formula, we can solve for PMT:
$0 = PMT * [(1 - (1 + 0.10)^-8) / 0.10]
Rearranging the formula to solve for PMT:
PMT = $40,000 / [(1 - (1 + 0.10)^-8) / 0.10]
Using a calculator, PMT should be around $3,686.18.
Therefore, Linda would need to put away approximately $3,686.18 annually to accumulate the required capital in eight years, considering she already has $10,000 saved.
d. Linda can use an investment plan to help reach her objective by following a few steps:
1. Set a specific goal: Linda has already set her goal of opening a bookstore in eight years and needing $50,000 in capital.
2. Determine the timeline: Linda has a clear timeline of eight years.
3. Calculate the required investment: Linda can calculate the required lump sum or annual investment using formulas like the future value or present value of an annuity, as mentioned earlier.
4. Establish an investment strategy: Linda needs to decide how much risk she is willing to take with her investments, considering the potential returns. She can consult with a financial advisor to determine a suitable investment strategy based on her risk tolerance and time horizon.
5. Review and adjust the plan: Linda should regularly review her investment plan and make adjustments based on progress, changes in income, or market conditions. She may also need to increase or decrease her annual investment amount depending on how her savings grow.
By following an investment plan, Linda can systematically save and invest to reach her goal of opening a bookstore in eight years.