Question 3 8 Marks Today an investment you made three years

Question 3: (8 Marks) Today an investment you made three years ago has matured and is now worth $3000. It was a three-year deposit, which bore an interest rate of 10%per year, compounded monthly. You knew at the time that you took a risk in making such an investment because interest rates vary over time and you \"locked in\" at 10% for three years. Hint: Download Interest Table spreadsheet from the course Resources folder. Round interest rates per year to three decimal places. i.e. 0.123 12.3% and dollars rounded to the nearest penny. a) How much was your initial deposit? (2 marks) b) Looking back over the past three years, interest rates for similar one-year investments did indeed vary. The interest rates were 8% for the first year, 10% for the second, and 14% the third (all compounded monthly). What would have happened if you had invested at these rates instead of locking in at 10%? How much money in total would you have gained or lost? (6 marks)

Solution

(a) Here, F = $3000

         i = 0.0083 (i.e. 0.10/12) Because interest is compounded monthly. So, 0.0083 is monthly interest.

         n = 36 (i.e. 12 x 3)

Therefore, Present value

        P = F / (1+i)ⁿ

           = 3000/(1+0.0083)³⁶

        P = 2227.17

If we round it, it becomes P = 2227

(b) At the end of 1st year, the future value at 8% interest will be

F = P(1+i)ⁿ = 2227(1+0.0067)¹² = $2412.80

At the end of 2nd year, the future value at 10% interest will be

F = P(1+i)ⁿ = 2412.80(1+0.0083)¹² = $2664.40

At the end of 3rd year, the future value at 14% interest will be

F = P(1+i)ⁿ = 2664.40(1+0.012)¹² = $3074.44

If we round it, it becomes $3074

If the amount had invested i these interest rates. one could have gained $74 (i.e.3074-3000).