Question

Imagine that you need to save $12,000. In this task, you will create and analyze investments to reach this goal.

A) Describe two possible financial goals for which you may require $12,000. Classify each as a want or a need.

B) Create and describe three possible investments to reach your goal within 5 years. Investment 1 is a simple interest investment with 3% annual interest. How much would you need to invest at the beginning? Investment 2 is a compound interest investment, with 3% annual interest compounded monthly. How much would you need to invest at the beginning? Investment 3 is a regular deposit in an account that earns 3% compound interest, compounded once per year. How much do you need to deposit, and how often will you deposit it, to reach your goal? State the details of the three investments and explain the pros and cons of each.

C) Calculate and describe the total interest earned on each of your three investments. Explain your thinking and show your work.​

Answer 1

A) Two possible financial goals for which you may require $12,000 are a want (saving for a vacation) and a need (saving for a down payment on a car).

B) Three possible investments to reach your goal within 5 years are Investment 1 (simple interest with 3% annual interest), Investment 2 (compound interest with 3% annual interest compounded monthly), and Investment 3 (regular deposits with 3% compound interest compounded once per year).

C) The total interest earned on each investment can be calculated using the formula: Total Interest = Principal + Goal - Total Deposits.

Step-by-step explanation:

A) Two possible financial goals for which you may require $12,000 are:

1. A want: Saving for a vacation.
2. A need: Saving for a down payment on a car.

B) Three possible investments to reach your goal within 5 years:

Investment 1: A simple interest investment with 3% annual interest.

To calculate how much you need to invest at the beginning, you can use the formula:

Principal = Goal / (1 + (Interest Rate x Time))

So for Investment 1, the principal would be $12,000 / (1 + (0.03 x 5))

= $12,000 / 1.15

= $10,434.78.

Investment 2: A compound interest investment, with 3% annual interest compounded monthly.

To calculate how much you need to invest at the beginning, you can use the formula:

Principal = Goal / (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods x Time)

For Investment 2, the principal would be $12,000 / (1 + (0.03 / 12))^(12 x 5)

= $12,000 / (1.0025)^(60)

= $10,409.97.

Investment 3: A regular deposit in an account that earns 3% compound interest, compounded once per year.

To calculate how much you need to deposit, and how often you need to deposit it, you can use the formula:

Deposit Amount = Goal / (((1 + Interest Rate)^(Number of Compounding Periods x Time)) - 1) / (Interest Rate x Number of Compounding Periods)

For Investment 3, if you want to make monthly deposits, the deposit amount would be $12,000 / (((1 + 0.03)^(1 x 5)) - 1) / (0.03 x 1)

= $12,000 / (1.1295 - 1) / 0.03

= $338.63 per month.

C) The total interest earned on each of your investments can be calculated using the formula:

Total Interest = Principal + Goal - Total Deposits

For Investment 1, the total interest would be $10,434.78 + $12,000 - $10,434.78

= $11,565.22.

For Investment 2, the total interest would be $10,409.97 + $12,000 - $10,409.97

= $11,590.03.

For Investment 3, the total interest would be ($338.63 x 60) + $12,000 - ($338.63 x 60)

= $12,000.