Time Value of Money. (1) Calculate future value or present value or annuity? (2) Future value = PV * (1+ i) n

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1 Problem 1 Happy Harry has just bought a scratch lottery tcket ad wo 10,000. He wats to face the future study of hs ewly bor daughter ad vests ths moey a fud wth a maturty of 18 years offerg a promsg yearly retur of 6%. What s the amout avalable o the 18th brthday of hs daughter? (1) Calculate future value or preset value or auty? Future value = PV * (1+ ) - PV = 10,000 - = 6% - = 18 years FV = 10,000 * = 10,000 * = 28, Problem 2 Rudy wll retre 20 years. Ths year he wats to fud a amout of 15,000 to become avalable 20 years. How much does he have to depost to a peso pla earg 7% aually? (1) Calculate future value or preset value or auty? FV Preset value = ( 1+ ) - FV = 15,000 - = 7% - = 20 years PV = 15,000 * (1/ ) = 15,000 * = 3, Nyerode Ceter for Face - Des Vk 1

2 Problem 3 The Natoal Savgs Fud promses a mothly 0.75% retur f you depost 100 per moth for 15 cosecutve years. What amout wll be accumulated after those 15 years? (1) Calculate future value or preset value or auty? (1 + ) 1 Future value = A* - Auty = = 15 years???!!! - = 0.75% p/m FVAN = 100 * ( ) / = 100 * = 37, Problem 4 Wlly has just bought a house. She estmates that the roof wll have to be reewed at a cost of 25,000 after 20 years. To cover these costs, she teds to save a equal amout of moey at the ed of each year, earg 6% aual terest rate. How much s such a yearly auty? (1) Calculate future value or preset value or auty? (1 + ) 1 Future value = A* - FV = 25,000 - = 20 years - = 6% (FVAN) 25,000 = A * ( ) / 0.06 <=> 25,000 = A * <=> A = 25,000/ = Nyerode Ceter for Face - Des Vk 2

3 Problem 5 Pete cosders buyg a house. Curretly, he rets a place for 1,000 a moth. The curret mothly terest rate o mortgages s 0.5%. Hs plag perod s 20 years. If he does t wat to crease hs housg costs, what amout of mortgage s avalable for hs purchase? (Neglect ay tax effects here). (1) Calculate future value or preset value or auty? 1 1 Preset value = (1 + ) A* - A = 1,000 - = 0.5% per moth - = 20??! PVAN = 1,000 * [( 1 (1/ )) / 0.005] = 1,000 * = 139, Problem 6 Lphps Ltd has just pad a dvded per share of Shares are valued oly o the bass of expected dvdeds. A aual sustaable growth of dvdeds of 4% s assumed. The approprate dscout rate () s 10% per year. The plag horzo s lmted to 20 years. Compute the share value. (1) Calculate future value or preset value or auty? Preset value = 1+ g 1 1+ A* g - A = 1.20*1.04 = = 10% aually - g = 4% aually - = 20 (PVGRAN) (1.20 * 1.04 ) * [1 ( / ) / ( )] => * = Nyerode Ceter for Face - Des Vk 3

4 Problem 7 Compute the share value of a compay payg a dvded of 3.60 per year over fte maturty, wth expected zero growth. The dscout rate () s assumed to be 12% yearly. (1) Calculate future value or preset value or auty? A Preset value = 3.60 / 0.12 = 30 Problem 8 Cetures ago, rch famles the provce of Freslad establshed a fud to further welfare ad educato. From ths fud, oly the terest reveue was allowed to be spet, order to keep the prcpal uattached. Assume the fud has amouted to 12 mllo ad market terest rate () s 6% aually. What would be the perpetuty (or preset value of the fud) edowed to the socety? (1) Calculate future value or preset value or auty? A Preset value = 0.06 * 12 mllo / 0.06 = 12 mllo. Nyerode Ceter for Face - Des Vk 4

5 Problem 9 Calculate the value of a costat cash flow of 500 a year wth a growth of 4%, measured over a fte perod at a dscout rate () of 10%. (1) Calculate future value or preset value or auty? 1 Preset value = A* g 500 * (1.04) / ( ) = 8, Problem 10 Compute the effectve yearly rate f the mothly rate s 1%. e m = m - omal (APR) => 1% * 12 = 12%. - effectve => ( )-1 (*100%) = 12.68%. Problem 11 Compute the quarterly terest rate cocerg a effectve aual rate of 12% ad a omal aual rate of 12%. Quarterly terest rate s: (1.12 (1/4) -1) *100% = 2.87% Addtoal: If the aual percetage rate s 12% cocerg mothly compoudg, what s the the effectve aual rate? [1 + (12%/12)] 12-1 =12.68%. e APR m = m Nyerode Ceter for Face - Des Vk 5

6 What s the the effectve rate for the frst quarter? [1 + (12%/12)] 3-1 = 3.03%. Problem 12 A compay buys a pece of equpmet for 2 mllo o Jauary 1. The expected useful lfe s 6 years ad the salvage value s estmated zero. The compay teds to replace the equpmet detcally. The average expected prce crease s 8% yearly. For ths purpose, the compay creates a specal fud wth aual equal paymets at the ed of each year durg the lfetme. Cost of captal ad eargs of the fud () s 10% per year. Compute the aual paymet to the fud. (1) Calculate future value or preset value or auty? (1 + ) 1 Future value = A* Prce at replacemet tme (or future value) => 2,000 x = 3,174 FVAN => 3,174 = A * [(1.1) 6-1] / 0.1 <=> A = 3,174 / = Nyerode Ceter for Face - Des Vk 6