*label*Mathematics

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Dear student,Please find enclosed a doc file containing the step by step solution to the different questions, together with an xls file with the different calculations. In the xls file, each question is presented as an independent worksheet so that you can find them easily

Question 1

a) Time value of money represents the actual value we give to money. It appears as a necessary

concept to understand why even while a $100 bill has the same monetary value both now and in

the future. This can easily be understood by considering that if we have the money available right

now, we would be able of investing it, such that in the future we would have both the available

money (the $100 bill) and the interests that have matured from it. This concept is further analysed

through the examples in section b.

b)

1. Since no further information is provided, we will assume a simple interest investment to evaluate

the future value. According to this, the relationship between the current and future value of money

would be given by the formula:

πππ¦π

πΉπ’π‘π’ππ π£πππ’π = πΆπ’πππππ‘ π£πππ’π (1 + ππππ’ππ πππ‘ππππ π‘ πππ‘π β

)

365

Taking this into account, we find:

Current value = $120

Interest rate = 7.5% annually

Time = 120 days

πΉπ’π‘π’ππ π£πππ’π = 120 (1 + 0.075 β

120

) = $122.96

365

2. Since we are told that there are no interest payments in the 7 year period, we should assume a

simple interest regime. Taking this into account, we would calculate the annual interest rate by

applying the formula

πΉπ’π‘π’ππ π£πππ’π

1

π=(

β 1) β

πΆπ’πππππ‘ π£πππ’π

ππ’ππππ ππ π¦ππππ

Taking this into account, we find:

1360.86

1

π=(

β 1) β = 5.16%

1000

7

3. Considering an annual interest rate of 12%, we can easily calculate the corresponding quarterly and

monthly interest rates by taking into account that one year has 3 quarters and 12 months. Thus,

the corresponding quarterly and monthly interest rates would be:

ππ’πππ‘ππππ¦ πππ‘ππππ π‘ πππ‘π =

ππππ‘βππ¦ πππ‘ππππ π‘ πππ‘π =

ππππ’ππ πππ‘ππππ π‘ πππ‘π 12

=

= 3%

4

4

ππππ’ππ πππ‘ππππ π‘ πππ‘π 12

=

= 1%

12

12

If we calculate the effective annual rates assuming it was compounded quarterly or monthly, we

would find:

π΄πππ’ππ πππ‘π (ππππππ’ππππ ππ’πππ‘ππππ¦) = (1 + 0.03)4 = 12.55%

π΄πππ’ππ πππ‘π (ππππππ’ππππ ππππ‘βππ¦) = (1 + 0.01)12 = 12.68%

Question 2

a) Some statistical concepts that are commonly used in finance include:

The mode, which represents the financial value that is repeated most frequently

The arithmetic mean, which is calculated by adding up all the financial va...

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