Question

QUESTION 31

On January 1, 2000 the price of gold was $282 per ounce. On January 1, 2013 the price was $1,890. What is the compound rate of growth in the price of gold over this period?

21.10%

19.17%

17.18%

none of the above

QUESTION 32

What is the monthly discount factor (or present value factor) at 3% for 30 years?

11.26%

19.60%

20.30%

21.33%

None of the above

Please solve both questions showing a step by step solution with formulas.

Answer 1

31.

We can compute rate of interest from relation of present value and future value as:

FV = PV x (1+r) ⁿ

FV = Future value = $ 1,890

PV = Present value = $ 282

r = Rate of interest

n = Number of periods = 1 Jan 2013 – 1 Jan 2000 = 13 years

$ 1,890 = $ 282 x (1+r) ¹³

$ 1,890 / $ 282 = (1+r) ¹³

(1+r) ¹³ = 6.70212765957447

1+r = 6.70212765957447^1/13

1+r = 6.70212765957447^{0.0769230769230769}

1+r = 1.15759015018012

r = 1.15759015018012 – 1 = 0.15759015018012 or 15.76 %

Compound rate of growth in price of gold over the period is 15.76 % annually.

Hence option “none of the above” is correct answer.

32.

PV factor = 1-(1+r)^-n/r

r = Rate of interest = 3 % or 0.03

n = Number of periods = 30

Substituting the values and solving, we get PV factor as:

PV factor = [1-(1+0.03)^-30]/0.03

                 = 1-(1.03)^-30/0.03

                 = (1-0.411986759515907)/0.03

                 = 0.588013240484093/0.03

                 = 19.6004413494698 or 19.60

Hence option “19.60” is correct answer. But % sign is not required.