CIMA BA1 · Chapter 13

The time value of money MCQs with Answers

10 multiple-choice questions on The time value of money for CIMA BA1 Fundamentals of Business Economics. Try each one before revealing the answer and explanation.

1. Question 1

   $8,000 is invested at 5% a year simple interest for 4 years. What will the investment be worth at the end of the period?

   • A) $9,724.05
   • B) $9,600.00
   • C) $1,600.00
   • D) $8,400.00
   Show answer & explanation

   Answer: B) $9,600.00

   Simple interest = 8,000 x 0.05 x 4 = $1,600.00. Value = 8,000 + 1,600 = $9,600.00. With compound interest it would be 8,000 x 1.05^4 = $9,724.05.

2. Question 2

   $5,000 is invested at 6% a year compound interest. What will it be worth after 3 years (to the nearest cent)?

   • A) $5,955.08
   • B) $5,900.00
   • C) $6,312.38
   • D) $5,300.00
   Show answer & explanation

   Answer: A) $5,955.08

   Future value = P x (1 + r)^n = 5,000 x 1.06^3 = 5,000 x 1.191016 = $5,955.08.

3. Question 3

   A loan charges interest of 2% per quarter, compounded quarterly. What is the effective annual rate of interest (to two decimal places)?

   • A) 8.00%
   • B) 6.12%
   • C) 2.00%
   • D) 8.24%
   Show answer & explanation

   Answer: D) 8.24%

   Effective annual rate = (1 + quarterly rate)^4 - 1 = 1.02^4 - 1 = 1.082432 - 1 = 8.24%. It exceeds 8% because interest is earned on interest within the year.

4. Question 4

   What is the present value of $12,000 receivable in three years' time if the discount rate is 8% a year (to the nearest cent)?

   • A) $9,120.00
   • B) $15,116.54
   • C) $9,525.99
   • D) $9,677.42
   Show answer & explanation

   Answer: C) $9,525.99

   PV = future value / (1 + r)^n = 12,000 / 1.08^3 = 12,000 / 1.259712 = $9,525.99.

5. Question 5

   What is the present value of $4,000 received at the end of each year for five years, discounted at 10% a year (to the nearest cent)?

   • A) $20,000.00
   • B) $15,163.15
   • C) $12,679.46
   • D) $16,679.46
   Show answer & explanation

   Answer: B) $15,163.15

   Annuity factor = (1 - (1.10)^-5) / 0.10 = 3.7908. PV = 4,000 x 3.790787 = $15,163.15 (calculated with the unrounded factor).

6. Question 6

   An investment will pay $3,000 a year in perpetuity, with the first payment received at the end of Year 3. If the discount rate is 6% a year, what is the present value of the investment (to the nearest cent)?

   • A) $44,499.82
   • B) $50,000.00
   • C) $47,169.81
   • D) $41,980.96
   Show answer & explanation

   Answer: A) $44,499.82

   A perpetuity starting at the end of Year 3 is valued at the end of Year 2 as 3,000 / 0.06 = $50,000.00. Discounting this two years to today: 50,000 / 1.06^2 = 50,000 / 1.1236 = $44,499.82.

7. Question 7

   A project requires an initial investment of $20,000 and is expected to generate net cash inflows of $8,000 at the end of each of the next three years. Using a cost of capital of 9% a year, what is the net present value (to the nearest dollar)?

   • A) $4,000
   • B) $2,073
   • C) -$250
   • D) $250
   Show answer & explanation

   Answer: D) $250

   Three-year annuity factor at 9% = (1 - 1.09^-3) / 0.09 = 2.5313. PV of inflows = 8,000 x 2.531295 = $20,250.36. NPV = 20,250.36 - 20,000 = $250 (rounded). The NPV is positive, so the project should be accepted.

8. Question 8

   A project has a net present value of +$2,400 at a discount rate of 10% and -$1,600 at a discount rate of 15%. Using linear interpolation, what is the estimated internal rate of return?

   • A) 12.0%
   • B) 12.5%
   • C) 13.0%
   • D) 25.0%
   Show answer & explanation

   Answer: C) 13.0%

   IRR = L + (NPV at L / (NPV at L - NPV at H)) x (H - L) = 10% + (2,400 / (2,400 + 1,600)) x 5% = 10% + 0.6 x 5% = 13.0%.

9. Question 9

   A business borrows $30,000 at 7% a year, to be repaid by four equal instalments at the end of each year. What is the amount of each instalment (to the nearest dollar)?

   • A) $7,500
   • B) $8,857
   • C) $9,600
   • D) $9,831
   Show answer & explanation

   Answer: B) $8,857

   The loan equals the present value of the instalments. Four-year annuity factor at 7% = (1 - 1.07^-4) / 0.07 = 3.3872. Instalment = 30,000 / 3.387211 = $8,857 (rounded).

10. Question 10

    A saver deposits $2,000 at the end of each year for five years in an account paying 5% a year compound interest. What is the balance immediately after the fifth deposit (to the nearest cent)?

    • A) $11,051.26
    • B) $10,000.00
    • C) $11,603.83
    • D) $8,658.95
    Show answer & explanation

    Answer: A) $11,051.26

    Future value of an annuity = A x ((1 + r)^n - 1) / r = 2,000 x (1.05^5 - 1) / 0.05 = 2,000 x 5.525631 = $11,051.26.