10.13 Some TVM Practice Questions
You will need to solve all these problems by hand. You will not be able to use the tables.
- You are given the following. Investment = $2,800, Rate = 0.54%, P = quarterly, N = 8 years. What is the Future Value?
- You are given two choices: 1. invest at an annual rate of 10% compounded monthly, or 2. at 10.1% compounded semi-annually. Which will you prefer?
- Bonus question: You will receive $24,000, $29,500, $58,000 and $87,000 each year consecutively for the next four years. What are both the Present- and Future-Values of this uneven income stream? Assume an annual rate of 4.6%. (We will learn how to do Uneven Cash Flows after we do Annuities – below.)
Solutions
1. ($2,800) (1 + 0.0054/4) 8 x 4 = $2,923.5256
2. First Choice: (1 + .10/12) 1 x 12 = 1.1047 This is the one.
Second Choice: (1 + .101/2) 1 x 2 = 1.1036
3. Present Value =
($24,000 ÷ 1.046 1) + ($29,500 ÷ 1.0462) + ($58,000 ÷ 1.0463) + ($87,000 ÷ 1.0464) =
$22,944.55 + $26,962.41 + $50,679.57 + $72,676.25 = $173,262.78
Future Value =
($24,000 × 1.0463) + ($29,500 × 1.0462) + ($58,000 × 1.0461) + ($87,000 × 1.0460) =
$27,466.69 + $32,276.42 + $60,668 + $87,000 = $207,411.11
Notice the nature of the exponents in the Future Value calculation; the exponents decrease as we near the horizon. Interestingly, it is also true that $173,262.78 ×1.046 (to the fourth) = $207,411.11. If you had already calculated the Present Value of this uneven series of cash flows, you would not have had to go through the long calculation of the Future Value.
(If you have trouble with this, it’s OK. We will get to Uneven Cash Flow series soon. You can come back to it later.)