Question

Question 1: Investor's Perspective (10 pts)

Let's assume that, now that you have neared the end of this unit, you are agreeable to investing some of your money in an account that will earn interest for you. Describe at least three ways that you can maximize the growth of your investment over time. Do the following calculations to help you determine what factors will help your money to grow, and use your results from these calculations in your response to this question.

• invest $5000 at 4.5% simple interest versus 4.5% compound interest (quarterly), and compare the results after 5 years
• invest $2500 at 4.5% compound interest versus $5000 at 4.5% compound interest, and compare results after 5 years with quarterly compounding
• invest $5000 at 4.5% compounded monthly versus 8% compounded monthly, and compare results after 5 years
• invest $5000 at 4.5% compounded monthly for 5 years versus 10 years, and compare results

Again, the purpose of this question is NOT for you to simply do calculations, but to analyze your results, and explain what you can do as an investor to help your money grow. Your response should be a paragraph with numbers in it, not simply numbers.

Question 2: Borrower's Perspective (10 pts)

When you take out a loan, you must pay interest rather than earning it. So, as a borrower, our goal is to pay as little interest as possible. In Question 1, you saw what will cause interest to be maximized. Now, reverse that, and think about what you would need to do as a borrower to minimize the amount of interest accruing on your loan. In your reply, explain how your choices in the following three areas could lower the amount of interest owed on the loan: 1) your loan principal (amount borrowed), 2) the loan's interest rate, and 3) the time required to pay back the loan.

Answer 1

Total amount after interest = Principal*(1+Annual interest rate/Compoundings per year)^(No. of years*Compoundings per year)

Investor's Perspective

a) Invest $5000 at 4.5% simple interest for 5 years

Total amount after interest = 5000*(1+ 0.045*5) = 6125

Invest $5000 at 4.5% compound interest (quarterly) for 5 years

Total amount after interest = 5000*(1+0.045/4)^(5*4) = 6253.75

b) invest $2500 at 4.5% compound interest

Total amount after interest = 2500*(1+0.045/4)^(5*4) = 3126.88

invest $5000at 4.5% compound interest

Total amount after interest = 5000*(1+0.045/4)^(5*4) = 6253.75

c) invest $5000 at 4.5% compounded monthly

Total amount after interest = 5000*(1+0.045/12)^(5*12) = 6258.98

invest $5000 at 8% compounded monthly

Total amount after interest = 5000*(1+0.08/12)^(5*12) = 7449.23

d) invest $5000 at 4.5% compounded monthly for 5 years

Total amount after interest = 5000*(1+0.045/12)^(5*12) = 6258.98

invest $5000 at 4.5% compounded monthly for 10 years

Total amount after interest = 5000*(1+0.045/12)^(10*12) = 7834.96

From an investor's perspective, the higher the interest income, the better it is since higher are the return on investment opportunities. In part a), we observe that compound interest is better than simple interest since there is a higher component of interest accumulated. In part b), we observe that the higher the principal, the more is the interest component. However, interest increases only proportionate to the amount lend, the percentage interest remains the same. In part c), we observe that the higher the rate of interest, the better is the interest-earning capability. In part d), a higher time frame signifies higher interest income for the investor due to the compounding effects.

Hence, to increase earnings, compound interest, higher time frame, and a higher rate of interest is recommended.

Borrower's Perspective

From an Borrower's perspective, the lower the interest income, the better it is since lower are the interest payments for the borrower. Conversely to the investor's perspective, simple interest would be a better option for the borrower. Also, lower the principal, lower is the absolute value of the interest accumulated. Lower rate of interest and lower the loan, better it is for the borrower. Hence, lower the loan pricipal,better it is. Lower the loan interest rate, better it is from the borrower'sperspective. Lower the time required to pay the loan, better it is for the borrower.