Math 373 Test 2 Fall 2014 March 11, 2014

Transcription

1 Math 373 Test 2 Fall 204 March, 204. Rendong is repaying a loan of 0,000 with monthly payments of 400 plus a smaller drop payment. Rendong is paying an annual effective interest rate of %. Determine the drop payment that Rendong will pay. () i (.) PV 0, 000 PMT 400 I / Y FV 0 CPT N nd AMORT: P=, P2=28 BAL= () i Drop ( )

2 2. Michael is receiving an annuity due with monthly payments for 20 years. Each monthly payment in the first year is 30. Each monthly payment in the second year is 260. Each monthly payment in the third year is 390. The payments continue to increase in the same pattern until each monthly payment in the 20 th year is Using an annual effective rate of interest of 7%, calculate the present value of this annuity. () i (.07) PV PV n m a nv n i P( )( ) m i m m a 20v i i ( )( ) a 20 (.07) (.07) v 20(.07) PV ( )( ) 42,

3 3. Dake is receiving a perpetuity due with annual payments. The payments are 000 at the beginning of each year except the payment at the beginning of every fifth year is In other words, the first four payments at 000 with the fifth payment being This is followed by four more payments of 000 and then a fifth payment of This pattern continues forever. Using an annual effective interest rate of 0%, calculate the present value of this perpetuity. You can break this into two perpetuities: One perpetuity is a perpetuity due with annual payments of 000. The other perpetuity is a perpetuity due with payments of 4000 every 5 years. () PV=P* ( i) 000( )(.0), 000 i 0.0 (2) PV=P* ( i) 4000 (.0) 7, (.0) ( ) 5 i 5 PV,

4 4. You are given the following table for the Trent Fund: Year Year2 Year 3 Year 4 Year 5 Portfolio Year i Kathy invests 0,000 on January, 2005 in the Trent Fund. Assuming that interest is determined using the investment year method, Kathy will have 5, on January, 203. Sarah invests 0,000 in the fund January, Assuming that Sarah is credited with interest using the portfolio method, calculate the amount that she will have on January, 203. Kathy: 0,000(.065)(.063)(.06)(.059)(.058)(.056)(+i)(.0525)=5, i= Sarah: 0, 000(.0705)(.068)(.065)(.06)(.056)( i)(.0525) 5,

5 5. A loan is being repaid with level monthly payments of The interest in the 40 th payment is The interest in the 70 th payment is Determine the amount of interest in the 40 th payment. PRIN PRIN ( i) i PRIN INT ( i)

6 6. Lingfeng is the beneficiary of an annuity immediate with annual payments of 500 for the next 20 years. Lingfeng takes each payment and invests the payment in Fund A which earns an annual effective interest rate of 4%. At the end of each year, Lingfeng withdraws the interest earned in Fund A and invests it in Fund B which earns an annual effective interest rate of 6%. At the end of 20 years, Lingfeng withdraws the amounts in both Fund A and Fund B. Determine that total amount that Lingfeng withdraws. (A) FV=500*20=30,000 (B) P=60, Q= FV=[60 a ( a 9 v )](.06) [60* ( ]( ) 6, TotalFV 6, ,

7 7. A loan of 00,000 is being repaid with geometrically increasing payments at the end of each year for 20 years. The first payment is Q. The second payment is Q (.05). The third payment is Q 2 (.05 ) year.. The payments continue to increase until The annual effective interest rate on the loan is 5%. Determine the amount of principal in the 9 th payment. 9 Q (.05 ) is paid at the end of the 20 th Qv Qv (.05) Qv (.05)... Qv (.05) 00,000 Qv Qv Qv... Qv 00,000 20Qv 00, Q( ).05 Q 5250 OLB Pmt v Pmt v Pmt Pmt OLB (.05), (.05) 3, Int OLB * i Prin Pmt Int, Prin

8 8. Choka Corporation borrows an amount of L to be repaid under the sinking fund method. Each year for 5 years, Choka will pay the interest on the loan and make a deposit into the sinking fund. The amount to be paid into the sinking fund is such that the sinking fund will be equal to L at the end of 5 years. The annual effective interest rate on the loan is 9% while the sinking fund will earn an annual effective interest rate of 7%. At the end of 5 years, the amount in the sinking fund is 84, Determine L. SF D* S 84, N=5, I/Y=7, PV=0, FV=84,529.54, CPT PMT=4, D D* S L PMT=D, I/Y=7, N=5, PV=0, CPT FV=369,

9 9. Wanling is receiving a deferred annuity with 20 annual payments. The first payment of 20,000 will be paid years from today. The second payment will be 20,000(.0). The third payment will be 20,000(.0 2 ). Each subsequent payment will be.0 times the prior payment. Using an annual effective interest rate of 5%, determine the present value of Wanling s annuity. PV 20, 000v 20, 000(.0) v 20, 000(.0) v... 20, 000(.0) v PV 20 2 st term - next term after last 20, 000v 20, 000(.0) v r.0v PV v 57,

10 0. Ross is receiving the following two annuities: a. A continuous annuity which pays at an annual rate of R for the next 20 years; or b. A continuous annuity which pays at a rate of 000t at time t for the next 20 years. The two annuities have the same present value at a force of interest of 8%. Determine R. e 0.08(20) 0.08(20) 20 a 20v 20e ( ) 000( 0.08 ) (20) e R( ) R

11 . A perpetuity makes annual payments at the end of each year. The first payment is 0,000. The second payment is Each subsequent payment decreases by 500 until the payment reaches Each payment thereafter is Calculate the present value of this perpetuity at an annual effective interest rate of 8%. PV ( I a) 5000a v 0,000, v PV 0, 000 a ( a 0 v ) PV 0, 000( ) 6250( ) 28, PV

12 . Pavel is receiving an annuity with quarterly payments for 25 years. The first payment is 0 at the end of the first quarter. The second payment is 40 at the end of the second quarter. The third payment is 60 at the end of the end of the third quarter. Each subsequent quarterly payment is 20 larger than the previous payment. Using an annual effective interest rate of 0%, calculate the accumulated value of this annuity. i 4 (4) 4 (.0) P=0, Q= FV=[0a ( a 00 v )]( ) FV [0( ) ( )]( ) FV 304,

13 3. Dias Corporation borrows 00,000 using a sinking fund loan to be repaid over 0 years. At the end of each year, Dias will pay the interest on the loan and make a deposit into the sinking fund. The deposit into the sinking fund will be determined such that amount in the sinking fund at the end of 0 years will exactly repay the loan. The interest rate on the loan is i and the interest rate earned by the sinking fund is 5%. The annual amount paid in interest is equal to the annual amount paid into the sinking fund. Determine i. L 00, 000 D S S I D I i * L , 000i i