In calculator: PV 4000 I/Y= N=12 PMT=348.13

Transcription

1 MATH 373 Test 1 Sprng 016 February 16, Courtney borrows 4000 to buy new sk equpment. She wll repay the loan wth level monthly payments over the next months. The loan has an annual effectve nterest rate of 8.4%. Calculate the amount of Courtney s monthly payment. () () (1 ) ( ) In calculator: PV 4000 I/Y= N= PMT= Or 4000 Pa 4000 P ( )

2 . Alan won the lottery. He wll receve annual payments at the begnnng of each year for 5 years. The frst payment wll be 50,000. The second payment wll be 50,000(1.1). The thrd payment wll be 50,000(1.1). The same pattern wll contnue wth each payment beng 110% of the prevous payment. Alan takes each payment and nvests t n a fund earnng an annual effectve nterest rate of 6.8%. Calculate the amount that Alan wll have at the end of 5 years FV 50, 000(1.068) 50, 000(1.1)(1.068) 50, 000(1.1) (1.068) 50, 000(1.1) (1.068) FV 50, 000(1.068) 50, 000(1.1) ,186, 73.40

3 1 3. You are gven that vt ( ) t Calculate Your answer needs to be accurate to 5 decmal places. 1 v( t) a( t) t at () a(10) a(9) (10) [1 0.04(9) ] a(9) (9) 4.4 a '( t) 0.08 t (0.08)(10) 0.8 t a( t) 10.04t 10.04(10)

4 4. Ben, Sammy, and Ian enter nto a fnancal agreement. Under the agreement, Ben wll pay Sammy 1000 today. Addtonally, Ben wll pay Ian 000 at the end of 3 years. Sammy wll pay Ian X at the end of years. Ian wll pay Ben at the end of 6 years. Under ths arrangement, Ben, Sammy, and Ian all have the same annual effectve yeld rate. Determne X. 6 3 Ben: 1000(1+ ) 000(1 ) CF 1000 CF 0 F CF 000 F CF 0 F CF F CPT IRR=8% Or x x x 3 (1 ) x a (1000) b b 4ac 000 (000) 4(1000)( ) x 3 1/3 (1 ) ( ) (1.08) X X

5 5. Shujng borrows money to buy a new car. The loan wll be repad wth monthly payments of The nterest rate on the loan s a monthly effectve rate of 1.5%. Rght after the th payment, the outstandng loan balance s 5, Determne the orgnal amount of the loan. OLB L(1 ) 1000s (1.015) 1 5, L(1.015) L (1.015) 1 5, (1.015) 3,55.33 Or OLB Qa 1000a nk n PMT 1000 I/Y=1.5% PV=5, ==> CPT N= n-=33 n=45 PMT 1000 I/Y=1.5% N=45 ==> CPT PV 3,55.34

6 6. You are gven that t. Hannah nvests 1000 today and 000 at the end of two years n an account earnng t t. Determne the amount that Hannah wll have at the end of 10 years FV 1,000e,000e ( t) dt ( t) dt [0.03 t t ] [0.03 t t ] FV 1,000e,000e 0 FV 4,965.40

7 7. Boyan borrowed 100,000 to be repad wth level monthly payments of 400 plus a drop payment. The annual effectve nterest rate on the loan s 9%. Determne the drop payment. () () 1 (1 0.09) In calculator: PV= -100,000 PMT=400 I/Y= CPT N= N=49 ND AMORT P1 1 P 49 BAL Drop (1733.7)( )

8 8. Magge borrows 5,000 from Jessca. The loan wll be repad wth three annual payments of Jessca renvests the payments at an annual effectve rate of r. After renvestment, Jessca realzes an annual effectve return of 7% on the loan. Determne r. 3 5, 000(1 0.07) (1 r) (1 r) (1 r) (1 r) 1, r ( )( 1, 006.5) ( ) r %

9 9. Yuje has 100,000 n her brokerage account on January 1, 013. On March 1, 013, she had an account balance of 105,000 pror to wthdrawng 40,000. On July 1, 014, Yuje deposted 5,000. Pror to that depost, she had a balance of 70,000. On December 31, 014, Yuje had a balance of 130,000 n her account. Usng the smple nterest rate approxmaton, estmate the annual dollar weghted return earned by Yuje. A C I B 100, 000 { 40, 000 5, 000} I 130, 000 I 130, 000 [100, 000 { 40, 000 5, 000}] 18, , 000 j ,000 40,0001 5, % 1 1/ 1 (1 j) T 1 ( ) %

10 10. Lews Industres s consderng two nvestments. The frst nvestment s the purchase of a perpetuty due wth annual payments. The cost of the perpetuty would be 1,000,000 and the annual payment would be 80,000. The second nvestment s buldng a new factory. To buld the factory, Lews would nvest 1,000,000 today to buld the factory. In return, he would expect to realze the followng profts at the end of each of the next four years: End of Year Proft 1 100,000 00, ,000 4 X The annual effectve nterest rate for the perpetuty s equal to the nternal rate of return for the new factory. Determne X. 1 1, 000, , 000a 80, , , , 000 x 1, 000, 000 where (1 ) (1 ) (1 ) x 596,385.19

11 11. Mengzh nvests 10,000 n an account earnng compound nterest. At the end of 10 years, Mengzh has 0,000. Cora nvests 4000 n an account earng smple nterest. At end of 8 years, Cora has Compound Let d 5 be the effectve dscount rate earned by Mengzh n the 5 th year. Smple Let 5 be the effectve nterest rate earned by Cora n the 5 th year. Smple Calculate 5 d 5 Compound. Your answer must be accurate to fve decmal places. 10, 000(1 d ) 0, 000 d Compound 10 Compound 5 5 4, 000(1 s 8) 8, 000 s 0.5 a( s) 1 0.5t Smple 5 a(5) a(4) a(4) d Smple Compound 5 5

12 . Penelope takes a loan to buy a car. She wll make 60 monthly payments of 350 to repay the loan but the payments are deferred wth the frst payment beng made at the end of months and the last payment beng made at the end of the 71 st month. Penelope s nterest rate s 9% compounded monthly. Determne the amount of Penelope s loan. () () PV v 350 a (1 ) 350 where = PV 15,530.9

13 13. Xn nvests 13,000 n an account for nne years. The account earns: a. An nterest rate equvalent to annual effectve dscount rate of 6% for the frst two years; b. A force of nterest of 0.08 for the next three years; and c. An nterest rate of 4% compounded quarterly for the last four years. Determne the amount n Xn s account at the end of nne years. (4) (4) FV d e 3 13,000(1 ) ( ) 1 4 (4) 44 FV 13, 000(1 0.06) ( e )(1 0.01) (0.08)(3) 16 FV 1,