2. Financial Maths

Question 1

The value of money depends on what?

Answer 1

On the point in time when the monetary flow (inflow/outflow) takes place.T

Question 2

The value of a future flow is higher than the value of a present flow.

Answer 2

FALSE

Question 3

Why is the value of a future flow lower than the value of a present flow?

Answer 3

Because
1. Giving up present consumption.
2. Giving alternative investment opportunities.
3. Default risk and inflation risk.

Question 4

Interest

Answer 4

Price or reward for giving up capital for a certain period of time..

Question 5

Interest rate

Answer 5

Price per unit of capital and time

Question 6

Simple interest

Answer 6

Interest payments will be received at the end of each period (and can be used freely). Interest earned only on the original capital invested C at t=0.

Question 7

Compound interest

Answer 7

Interests will be received at the end of the operation. Interest earned on interest.

Question 8

Simple interest for fractional time periods m (i*).

Answer 8

It is equivalent to a simple annual rate (i).

The total amounts paid at the end of the operations are the same –> i*=i/m.

Question 9

for a semester, m=?

Answer 9

m=2.

Question 10

for a quarter, m=?

Answer 10

m=4

Question 11

for a month, m=?

Answer 11

m=12

Question 12

Using compound interest, the total investment grows…

Answer 12

…at the end of each period, since interests are accumulated.

Question 13

Using compound interest, interest rate applies to…

Answer 13

…the principal + the interests perceived so far.

Question 14

Using compound interest, total interests generated during the lifetime of the loan:

Answer 14

C(1+i)^(N)-C

Question 15

Compound interest for fractional time periods (im).

Answer 15

It is equivalent to the compound annual rate (i).

The total amounts paid at the end of the operations are the same: im=(1+i)^(1/m)-1

Question 16

What is the AER (Annual Equivalent Rate)?

Answer 16

i=(1+im)^m-1 is the AER to a compound interest for fractional time periods im.

It is also known as the effective rate.

Question 17

V0 today is equivalent to…

Answer 17

…(1+i)*NV0 in N periods.

Question 18

V0 is the present value of…

Answer 18

…(1+i)*NV0 received in N periods.

Question 19

(1+i)*NV0 is the future value in N periods equivalent to…

Answer 19

…investing V0 today.

Question 20

What is an annuity?

Answer 20

A stream of equally spaced payments (A0,A1,A2,…,AN) increasing over time at a rate f; i.e. At=At-1(1+f), for a limited period of time.

Question 21

In the case of loans with constant annuities…

Answer 21

…payments are constant; i.e. the amount equivalent to principal + interest payments remain constant.