Question

4. This question consists of four main parts. When performing the calculations, keep as many decimal places as you can for intermediate answers, but round your final answers to two decimal places.           (13 marks total)

1. If you save $200 per month for 10 years at 12% annual percentage rate with monthly compounding,
   1. what is the future value annuity factor?                                       (1 mark)
   2. what is the future value?                                                         (1 mark)
2. Suppose that you have a choice between receiving $10,000 now and receiving $1000 per month for the next 12 months. Assuming that you can invest at a 12% annual percentage rate (APR) with monthly compounding, what is
   1. the present value annuity factor?                                               (1 mark)
   2. the present value?                                                                 (1 mark)
   3. your choice?                                                                         (1 mark)
   4. the break-even annual rate of return at which you are indifferent between receiving $10,000 now and receiving $1000 per month for 12 months?
                                                                                             (2 marks)
   5. the break-even number of monthly payments at which you are indifferent between receiving $10,000 now and receiving $1000 per month, given an APR of 12% with monthly compounding?          (1 mark)
   6. the break-even dollar amount of monthly payments, given an APR of 12% with monthly compounding and 12 months of payments?                                                                           (1 mark)

(Hint: Use the financial calculator for parts (iv), (v), and (vi). Clearly show the inputs you use for each calculation.)

3. You are saving $200 per month at 6% annual percentage return (APR) with monthly compounding. How many years will it take for your savings to accumulate to $10,000? (Hint: Use the financial calculator for this calculation, and clearly show the inputs you use.)                                                                                      (2 marks)
4. You are saving $200 per month. What annual percentage rate of return must be earned for your savings to accumulate to $30,000 in 10 years?                                                                             (2 marks)

Answer 1

a. i. Future value annuity factor = [ { ( 1.01 ) ¹²⁰ -1 } / 0.01 ] = 230.04

ii. Future value = $ 200 x 230.04 = $ 46,008.

b. i. Present value annuity factor = [ { 1 - ( 1 / 1.01 ) ¹² } / 0.01 ] = 11.2551

ii. Present value = $ 1,000 x 11.2551 = $ 11,255.10

iii. $ 1,000 per month.

iv. Break-even annual rate of return at which you would be indifferent : 35 %

PVIFA = [ { 1 - ( 1 / 1.02917 ) ¹² } / 0.029167 ] = 10

Present value of $ 1,000 per month = $ 1,000 x 10 = $ 10,000.