Question

1. The future value of a present sum increases as either the discount rate or the number of periods per year increases, other things held constant.

True

False

2. It is always desirable to have a higher compounding frequency, regardless of the initial investment or the time horizon.

True

False

3. The present value of a future sum increases as the term (N) increases, regardless of compounding frequency.

True

False

4. A perpetuity is a level stream of evenly spaced cash flows that never ends.

True

False

Answer 1

1.

Future value of present sum consistent of two components i.e. investment amount and interest earned during the investment period. Interest amount increases as interest rate or number of periods increases; consequently, future value also increases.

Example:

FV = PV x (1+r/m) ^{m x t}

PV	Rate (r)	Years (t)	Compounding frequency (m)	(1+r/m) m x t	FV
$ 1,000	0.06	1	1	1.06	$ 1,060.00
$ 1,000	0.1	1	1	1.10	$ 1,100.00
$ 1,000	0.06	1	12	1.061677812	$ 1,061.68

As we can observed future value of $ 1,000 increased with the increase of r and m.

Hence the statement is true.

2.

Higher compounding frequency will give a higher future value with the constant investment amount and time. Hence for investment purposes higher compounding frequency is preferred.

The statement is true.

3.

Present value of a future sum is inversely proportional with the term (i.e. number of periods).

On increasing the terms, present value decreases with constant compounding frequency.

Example:

PV = FV/(1+r) ⁿ

FV	r	n	(1+r) n	PV
$ 1,000	0.05	5	1.276281563	$ 783.53
$ 1,000	0.05	10	1.628894627	$ 613.91

As we can observed present value of $ 1,000 decreased with the increase of n.

Hence the statement is false.

4.

A perpetuity is a stream of cash flow that continues for an infinite period of time.

Hence the statement is true.