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# Time Value and Loan Amortization

INSTRUCTIONS TO CANDIDATES

1 Numpy: Time Value and Loan Amortization

2 Time Value

2.1 Present value

2.2 Future value

3 Value at the end of a specified year

4 Writing a function to compute the present value at the end of a year

5 Loan payments and amortization

0.1 Numpy: Time Value and Loan Amortization

0.2 Time Value

int_rate=4.00%

[3]:

[[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]]

[4]:

[[ 0.00 1.00 2.00 3.00 4.00]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0

[5]:

[[ 0.00 1.00 2.00 3.00 4.00]

[ 100.00 175.00 250.00 325.00 400.00]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]]

[6]:

[[ 0.00 1.00 2.00 3.00 4.00]

[ 100.00 175.00 250.00 325.00 400.00]

[ 1.00 1.04 1.08 1.12 1.17]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]]

0.2.1 Present value

[7]: # Row 3 of the

print(pvfv) pvfv array = Row 1 / Row 2

[[ 0.00 1.00 2.00 3.00 4.00]

[ 100.00 175.00 250.00 325.00 400.00]

[ 1.00 1.04 1.08 1.12 1.17]

[ 100.00 168.27 231.14 288.92 341.92]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]]

[9]:

1130.2537770036063

0.2.2 Future value

[[ 0.00 1.00 2.00 3.00 4.00]

[ 100.00 175.00 250.00 325.00 400.00]

[ 1.00 1.04 1.08 1.12 1.17]

[ 100.00 168.27 231.14 288.92 341.92]

[ 4.00 3.00 2.00 1.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]

[ 0.00 0.00 0.00 0.00 0.00]]

[10]: # Set  row 5 = (1+int_rate) raised to row 4

print(pvfv)

[[ 0.00 1.00 2.00 3.00 4.00]

[ 100.00 175.00 250.00 325.00 400.00]

[ 1.00 1.04 1.08 1.12 1.17]

(5/5)

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