Question

Part B – Long Answer Questions                                                                                                         

Question 1

You are a young personal financial adviser. Diana, one of your clients approached you for consultation about her personal financial plans to get $50,000 for a European 1-month holiday. Diana has a saving of $30,000 and is considering two alternative options:

Option 1: Investing that $30,000 in an investment that would pay a rate of return of 8% annually, compounding semi-annually for 5 years.

Option 2: Obtaining a personal loan of $20,000 from a bank to take the European 1-month holiday now and pay the debt in 5 years. The current interest rate the bank offered for the new personal loan is 5% annually, compounding monthly.

Required:

1. Compute the effective annual interest rate (EAR) Diana would actually get in Option 1.
   (2.5 marks)
2. Calculate the amount of money Diana would accumulate in Option 1 after 5 years.(2.5 marks)

3. ANSWER:

4. How much longer does Diana need to wait until she has $50,000 to get her dream holiday in Option 1? (2.5 marks)

5. ANSWER:

6. Calculate the monthly debt repayment Diana needs to pay the bank for 5 years in Option 2.
   (2.5 marks)
7. ANSWER:

8.  

    

    

    

Answer 1

a. effective annual interest rate (EAR) in Option 1 = (1 + i/m)^m - 1

i = interest rate; m = compounding frequency

compounding frequency is semi-annual which is 2 times in a year.

effective annual interest rate (EAR) in Option 1 = (1 + 0.08/2)² - 1 = (1 + 0.04)² - 1 = 1.04² - 1 = 1.0816 - 1 = 0.0816 or 8.16%

the effective annual interest rate (EAR) Diana would actually get in Option 1 is 8.16%.

b. money accumulated after 5 years = investment amount*(1+interest rate/2)^{no. of years*2}

2 is for semi-annual compounding frequency.

money accumulated after 5 years = $30,000*(1+0.08/2)^2*5 = $30,000*(1+0.04)¹⁰ = $30,000*1.04¹⁰ = $30,000*1.48024428491834392576 = $44,407.33

the amount of money Diana would accumulate in Option 1 after 5 years is $44,407.33.

d. we can use financial calculator for calculation of time required to get $50,000 with below keystrokes.

PV = present value = -$30,000; I/Y = semi-annual interest rate = 8%/2 = 4%; PMT = interest payment = $0; FV = future value = $50,000 > CPT = compute > N = semi-annual period = 13.02

PV needs to be entered as negative value as it's a cash outflow.

no. of years = semi-annual period/2 = 13.02/2 = 6.51 Years

Diana needs to wait 6.51 years until she has $50,000 to get her dream holiday in Option 1.

f. we can use financial calculator for calculation of monthly debt repayment with below keystrokes.

PV = loan amount = $20,000; I/Y = monthly interest rate = 5%/12 = 0.4167%; N = no. of months = 5*12 = 60; FV = future value = $0 > CPT = compute > PMT = monthly debt repayment = $377.42

Calculator will display PMT as negative value as it's a cash outflow.

the monthly debt repayment Diana needs to pay the bank for 5 years in Option 2 is $377.42.