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Biem 18 a.y 19/20 Self-assesment Test: Financial laws, Annuities, Amortization, consumer credit, leasing

1) Given a principal C=100 calculate the final value after 340 days at i= 2% compound 2) 1230 is the present value of 1300 due in 1.2 years. Calculate the annual discount rate 3) A principal C is invested over 2 years at simple interest i= 2% and then reinvested over 3 years at advance dimple interest with annual discount rate d. Provide the expression of the final value after 5 years 4) Calculate the equivalent annual compound rate of the financial operation in question 3 for d= 3% 5) Given i= 4% annual compound calculate the monthly interest rate and the nominal annual interest rate convertible 12 times a year. 6) Calculate the force of interest of f (t )  1  0.01t  0.001t2 and say if f(t) is decomposable 7) Calculate the discounted value of 1000 due in 3.5 years using the financial law of question 6 2

 8) Given the two variable financial law F ( x, y)  e0.01( y x) , calculate the force of interest and deduce whether the financial law is decomposable 9) Calculate the final value of 1000 invested at x= 2 over 4 years using the financial law of question 8. 10) Considering the financial operation of question 9, calculate the equivalent simple rate 11) Given the force of interest  ( x, y )  0.01x , calculate the final value of 1000 from 4 to 8.

12) Given the investment 13) Given the annuity

yrs amount

0 1.5 2 , say if the IRR is smaller than 2% 350 50 310

yrs

1 1.5 2 2.5 , calculate the final value at i= 2% annual amount 50 50 50 50

compound 14) Calculate the present value of the annuity due with 10 monthly instalments R=10 at the nominal annual interest rate of 10% 15) A loan S is repaid with 8 semi-annual constant instalments R =150 at i=4% annual compound. Calculate S 16) Considering the amortization in question 15, calculate the residual debt after 4 payments and calculate the principal quota of the 5th payment. 17) A loan S is repaid with 10 monthly instalments at constant principal quota 50. Calculate S 18) Considering question 17, calculate the residual debt after 8 payments 19) A loan amount of 10,000 is repaid with 10 annual instalments. Assuming that the first 9 instalments are equal to 800 , calculate the last instalment in order to have an internal rate of 2% annual

20) A Tv set is sold on instalments at the following conditions: price 5000, down-payment 10% of the price, 4 constant semi-annual payments at j 2 =10%. Calculate the constant instalment 21) Adding extra fees to question 20 the annual global compound cost is 13%. Calculate the new constant instalment. 22) A leasing contract has the following conditions: maturity 1 year, price 10,000, downpayment 20% of the price, 10 monthly constant fees, redemption fee 25% of the price at maturity, nominal annual rate 12%. Calculate the constant fee 23) Considering question 22, calculate the residual debt immediately after the second constant payment. 24) Considering question 22, calculate the residual debt immediately after 8th constant payment. 25) Considering question 22 recalculate the last 2 constant fees if after the 8th payment the interest rate becomes 13% annual compound.

Answers 1)

M  100(1.02)(340/365) =101.8617

2) 1230  1300(1  d1.2) =4.487%

 1  M  C(1  2%  2)    1  3d  5 4) 1.1428C= (1  i) , i= 2.70% 3)

(1/12)  1 =0.3274% , j 12  12  i 12 = 3.92% 5) i12  1.04

6)

 (t ) 

0.01  0.002 t , f(t) is not decomposable 1  0.01t  0.001t 2

1000 =954.88 f (3.5)  ( x, y )  0.02( y  x ) , f(x,y) is not decomposable 8) 9) 1000F (2, 4) =1173.511 7)

10) 1000F (2, 4)  (1  2i)

i=4.33%

11) 1000F (4,8) =1173.51 12) I NPV (2%)  350  13) 50 14) 10

50 350...