Finance Practice Problems

Transcription

1 Iteest Fiace Pactice Poblems Iteest is the cost of boowig moey. A iteest ate is the cost stated as a pecet of the amout boowed pe peiod of time, usually oe yea. The pevailig maket ate is composed of: 1. The Real Rate of Iteest that compesates ledes fo postpoig thei ow spedig duig the tem of the loa. 2. A Iflatio Pemium to offset the possibility that iflatio may eode the value of the moey duig the tem of the loa. A uit of moey (dolla, peso, etc) will puchase pogessively fewe goods ad sevices duig a peiod of iflatio, so the lede must icease the iteest ate to compesate fo that loss.. 3. Vaious Risk Pemiums to compesate the lede fo isky loas such as those that ae usecued, made to boowes with questioable cedit atigs, o illiquid loas that the lede may ot be able to eadily esell. The fist two compoets of the iteest ate listed above, the eal ate of iteest ad a iflatio pemium, collectively ae efeed to as the omial isk-fee ate. I the USA, the omial isk-fee ate ca be appoximated by the ate of US Teasuy bills sice they ae geeally cosideed to have a vey small isk. Simple Iteest Simple iteest is calculated o the oigial picipal oly. Accumulated iteest fom pio peiods is ot used i calculatios fo the followig peiods. Simple iteest is omally used fo a sigle peiod of less tha a yea, such as 30 o 60 days. F = P (1 + t) I = A - P I = P t F: Futue Value of the ivestmet P: picipal (iitial value of a ivestmet) : aual iteest ate i pecetage (%) I: iteest afte t yeas. Example 1:Michelle ivested $ i mutual fud with the iteest ate of 4.8%. How much iteest would she ea afte 2 yeas? Aswe : P = $ = 4.8% t = 2 I = P t I = ($ )(4.8%)(2) = $ Hece, Michelle would ea $480 afte 2 yeas. Example 2. Jeff has oe savigs accout with the iteest ate of 3.3%, ad oe moey maket accout with the iteest ate of 5.1% i a bak. If he deposits $ to the savigs accout, ad $ to the moey maket accout, how much moey will he have afte 6 yeas? Aswe: Savigs accout: 1

2 P = $ = 3.3% t = 6 F = P(1 + t) F = ($ )[1 + (3.3%)(6)]= ($ )(1.198)= $ Moey maket accout: P = $ = 5.1% t = 6 F = P(1 + t) F = ($ )[1+(5.1%)(6)] = ($ )(1.306) = $ Total amout: $ $ = $ Hece, Jeff will have $ afte 6 yeas. Compoud Iteest F = P(1 + ) t Compoud iteest is calculated each peiod o the oigial picipal ad all iteest accumulated duig past peiods. Although the iteest may be stated as a yealy ate, the compoudig peiods ca be yealy, semiaually, quately, o eve cotiuously. You ca thik of compoud iteest as a seies of back-to-back simple iteest cotacts. The iteest eaed i each peiod is added to the picipal of the pevious peiod to become the picipal fo the ext peiod. Fo example, you boow $10,000 fo thee yeas at 5% aual iteest compouded aually: iteest yea 1 = p * i * = 10,000 *.05 * 1 = 500 iteest yea 2 = (p 2 = p 1 + i 1 ) * i * = (10, ) *.05 * 1 = 525 iteest yea 3 = (p 3 = p 2 + i 2 ) * i * = (10, ) *.05 * 1 = Total iteest eaed ove the thee yeas = = 1, Compae this to 1,500 eaed ove the same umbe of yeas usig simple iteest. The powe of compoudig ca have a astoishig effect o the accumulatio of wealth. This table shows the esults of makig a oe-time ivestmet of $10,000 fo 30 yeas usig 12% simple iteest, ad 12% iteest compouded yealy ad quately. Type of Iteest Picipal Plus Iteest Eaed Simple 46, Compouded Yealy 299, Compouded Quately 347,

3 Example 1: Alex has $ i his moey maket accout cuetly. If the aual iteest ate os 3.9%, ad the iteest is compouded biweekly, how much moey was i his accout 2 yeas ago? (1 yea = 52 weeks) Aswe: F = $ = 3.9% = 26 t = 2 F = P(1 + ) t $ = P{[1 + (3.9% / 26)] (26)(2) } = P[( ) 52 ] = P( ) P = $ / = appoximately $ Hece, $ wee i Alex's accout 2 yeas ago. Example: Emily opes a savigs accout i a bak with the aual iteest ate of 2.7%. If she deposits $ to the accout, ad the iteest is compouded cotiually, how much iteest will she ea afte 4 yeas? Aswe: P = $ = 2.7% t = 4 I = P (e t - 1) I = ($ )[e (2.7%)(4) - 1] = ($ )(e ) = apposimately $ Hece, Emily will ea $ afte 4 yeas. 3

4 Odiay Auity (Sikig Fud ) Paymet at the ed of each peiod F = R t 1+ 1 Example: Joe deposits $22,000 at the ed of each yea fo 7 yeas, i a accout payig 6 % compouded aually, how much will he have o deposit afte 7 yeas? As: $184, Pactice 1: Mia deposits $500 at the ed of each moth fo 10 yeas, i a accout payig 5% compouded mothly, how much will she have o deposit afte 10 yeas? Pactice 2: Napoleo deposits $1,200 at the ed of each quate fo 10 yeas, i a accout payig 8 % compouded quately, how much will he have o deposit afte 10 yeas? As: $72, Pactice 3-a: Jose wats to etie i twety yeas ad fo this pupose he is depositig $200 at the ed of each moth i a sikig fud that pays 7.2% compouded mothly. If he will be doig this fo twety yeas, the how much moey will be thee fo him whe he eties? As: $106, Pactice 3-b: If Joe wats to accumulate $130,000 i the twety yeas peiod, ad the what iteest ate would povide that amout? As: 8.79% Pactice 4: Fid the amout of paymet to be Joe eeds to make ito a sikig fud evey quate to accumulate $62,000 afte 6 yeas: Kowig that moey eas 8 % compouded quately. As: $2, Pactice 5: Fid the amout of paymet to be made ito a sikig fud to accumulate $75,000 fo 4 ad half yea: moey eas 6% compouded semiaually. As: $7, t F = R R Auity Due Paymet at the begiig of each peiod Example: Joe deposits $500 at the begiig of each quate ed fo 7 yeas, i a accout payig 12 % compouded quately, how much will he have o deposit afte 7 yeas? As: $22,

5 Example: Joe deposits $500 at the ed of each quate fo 7 yeas, i a accout payig 12 % compouded quately, how much will he have o deposit afte 7 yeas? As: $21, Pactice 1: Cesa deposits $16,000 at the begiig of each yea fo 8 yeas, i a accout payig 4.7 % compouded aually, how much will he have o deposit afte 8 yeas? As: $158, Pactice2: Cesa deposits $100 at the begiig of each quate fo 30 yeas, i a accout payig 4 % compouded aually, how much will he have o deposit afte 8 yeas? As: Pactice 3: Fid the amout of paymet to be Joe eeds to make ito a auity fud evey quate to accumulate $62,000 afte 6 yeas: Kowig that moey eas 8 % compouded quately. As: Pactice 4: Fid the amout of paymet to be made ito a auity fud to accumulate $75,000 fo 4 ad half yea: moey eas 6% compouded semiaually. As: Amotizatio R = P 1 1+ t P = Loa Amout R = Peiodic Paymet = Iteest Rate = Compoudig Peiod t = Time Example (4-yea paymet): A ca costs $22,000. Afte a dow paymet of $4,000, the balace will be paid off i 48 equal mothly paymets with the iteest of 12 % pe yea o the upaid balace. Fid the amout of each paymet. As: $ Pactice 1 (5-yea tem): A ca costs $22,000. Afte a dow paymet of $4,000, the balace will be paid off i 60equal mothly paymets with the iteest of 12 % pe yea o the upaid balace. Fid the amout of each paymet. As: Pactice 2 (6-yea tem):a ca costs $22,000. Afte a dow paymet of $4,000, the balace will be paid off i 72 equal mothly paymets with the iteest of 12 % pe yea o the upaid balace. Fid the amout of each paymet. As: 5

6 Pactice 3 (Bad cedit): A ca costs $22,000. Afte a dow paymet of $4,000, the balace will be paid off i 48 equal mothly paymets with the iteest of 18% pe yea o the upaid balace. Fid the amout of each paymet. As: Pactice 4 (Good Cedit ad 4-yea tem): A ca costs $22,000. Afte a dow paymet of $4,000, the balace will be paid off i 48 equal mothly paymets with the iteest of 6% pe yea o the upaid balace. Fid the amout of each paymet. As: Pactice 5 (Bad Cedit ad 5-yea tem): A ca costs $22,000. Afte a dow paymet of $4,000, the balace will be paid off i 60 equal mothly paymets with the iteest of 18% pe yea o the upaid balace. Fid the amout of each paymet. As: Pactice 6 (Bad Cedit ad 7-yea tem): A ca costs $22,000. Afte a dow paymet of $4,000, the balace will be paid off i 72 equal mothly paymets with the iteest of 18% pe yea o the upaid balace. Fid the amout of each paymet. As: Additioal Poblems 1) How may days will it take fo a sum of $1,500 to ea $25 iteest if it is deposited i a bak payig 5% a yea?(use a 365- day a yea.) As: days 2) How log will it take a ivestmet of $5,000 to tiple if the ivestmet eas iteest at the ate of 8 % a yea compouded quately? As: yeas 3) Today, the pice of a gallo of milk is $4.25, assumig iflatio ate to be 4.5 % a yea. What will be the pice of a gallo of milk 10 yeas fom ow? As: $6.67 4) Five ad half yeas ago, Chis ivested $10,000 i a etiemet fud that gew at the ate of % pe yea compouded quately. What is his accout woth today? As: $17,

7 5) 5 yeas ago, Johy Cash ivested a sum of moey i a savig accout with iteest of 8 % pe yea compouded quately. His ivestmet is ow woth $22, How much did he oigially ivest? As: $15,000 6). Fid the futue value of odiay auity fo $150 pe moth fo 15 yeas at 10 % pe yea compouded mothly? As: $62, ) Fid the peset value of odiay auity fo $150 a moth at 8 % pe yea compouded quately fo 10 yeas? As: $4, ) If you cotibute $5,000 a yea ito a tust accout, the how much will be i the accout afte 25 yeas if the accout eas iteest at the ate of 8.5 % pe yea compouded yealy? As: $38, ) Pope ivested oly $24,000 i a etiemet fud 5 yeas ago. Today his ivestmet is woth $ Fid the effective aual ate of etu o his ivestmet ove 5-y peiod. As: 10) Fid the ate of iteest pe yea compouded o a daily basis that is equivalet to 9.6 % pe yea compouded mothly. As: 11) If $54,000 is ivested at a iteest ate of 9% fo 7.5 yeas compouded cotiuously, the fid its futue value. As: $106, ) Fid the mothly house paymets fo a loa of 188,000 at 5.74% fo 15 yeas As: $2, ) Fid the futue value of a auity of $672 deposited at the begiig of each quate fo 7 yeas at 8% compouded quately. As: $24,

8 14) A compay has odeed 20 ew PCs at a cost of $1800 each. They will ot be deliveed fo 5 moths. What amout should the fim deposit i a accout payig 8.1% to have eough moey to pay fo them? As: $34, ) A pack-a-day smoke speds about $120 pe moth o cigaettes. Suppose the smoke ivests that amout at the ed of each moth i a savigs accout at 6.7 % compouded mothly. What would the accout be woth afte 45 yeas? As: $413, ) The Blues Clues family bought a house fo $315,000. they paid $20,000 dow ad took out a 30-yea motgage fo the balace at 7%. Fid thei mothly et. As: $1, ) Fid the total iteest Blues Clues family will pay. As: $391, ) Fid the amout of each paymet that must be paid ito a sikig fud to accumulate $ 6,000 at 8% compouded mothly fo 3 yeas. As: $ ) If moey ca be boowed at 8 % compoud mothly, which oe is lage: $10,000 ow o $15,000 i 5 yeas? Use peset value to decide. As: $15,000 i 5 yeas 20. Oe of us classmates eeds to boow $18,000 fo 1 yea. He has bee offeed a loa with iteest compouded mothly ad a compoud amout of $19, Fid the ate. As: 10.34% 21) Billy Jea Kig deposited $6500 i a accout payig 7.5 %compouded quately. Afte 3 yeas the ate dops to 4% compouded semiaually. Fid the amout i he accout at the ed of 7 yeas. As: $9, ) Fo oe yea, a studet loa of $52,000 at 9% compouded semiaually esulted i a matuity value of $5, As:1.96 yea, 1y,11moths 8

9 23) Bobby Cash deposited $10,000 at 8% compouded quately. Two yeas afte she makes the fist deposit, he adds aothe $20,000, also at 8% ate compouded quately. What total amout will he have 4 yeas afte his fist deposit? As: $37, ) Bobby Cash deposited $10,000 at 8% compouded quately. Two yeas afte she makes the fist deposit, he adds aothe $20,000, also at 8% ate compouded quately. What total amout will he have 6 yeas afte his fist deposit? As: $ ). Joh ad Jill have $20,000 cash fo the dow paymet of a house ad they ca affod a 15-yea motgage paymet of $2,500/moth. If the best motgage ate that they ca get is 7.5% the what will be the most affodable home that they ca buy by thei cuet budget pla? As:$269, ,000 = $289, = $290,000 26) Adam ad Eve eed to boow $115,000 to puchase a cave ad ae debatig whethe they should use a 20-yea motgage o 30-yea motgage. They also wat to kow the effect of two iteest ates, a 6% ad 8%, o a) Mothly paymet b) Total cost ad c) Total iteest paid a) Mothly paymet Iteest ate Tem of the motgage 6% 8% 20 yeas $ $ yeas $ b) Total cost Iteest ate Tem of the motgage 6% 8% 20 yeas $197, $232, yeas $248,400 $303,876 c) Total iteest paid Iteest ate Tem of the motgage 6% 8% 20 yeas $82,616 $117, yeas $133,400 $188,876 9