Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 89385 by pete last updated on 17/Apr/20

Commented by pete last updated on 17/Apr/20

I need help on the above question, please.

$$\:\mathrm{I}\:\mathrm{need}\:\mathrm{help}\:\mathrm{on}\:\mathrm{the}\:\mathrm{above}\:\mathrm{question},\:\mathrm{please}. \\ $$

Answered by Joel578 last updated on 17/Apr/20

First option PV_1 = 48000v^6 + 11300v^(10) = $ 48607.51 Second option PV_2 = X + 12100v^8 = $ (X + 9551.85) Now, PV_1 = PV_2 ⇒ $ 48607.51 = $ (X + 9551.85) ⇒ X = $ 39055.65

$$\mathrm{First}\:\mathrm{option} \\ $$$${PV}_{\mathrm{1}} \:=\:\mathrm{48000}{v}^{\mathrm{6}} \:+\:\mathrm{11300}{v}^{\mathrm{10}} \:=\:\$\:\mathrm{48607}.\mathrm{51} \\ $$$$ \\ $$$$\mathrm{Second}\:\mathrm{option} \\ $$$${PV}_{\mathrm{2}} \:=\:{X}\:+\:\mathrm{12100}{v}^{\mathrm{8}} \:=\:\$\:\left({X}\:+\:\mathrm{9551}.\mathrm{85}\right) \\ $$$$ \\ $$$$\mathrm{Now}, \\ $$$${PV}_{\mathrm{1}} \:=\:{PV}_{\mathrm{2}} \\ $$$$\Rightarrow\:\$\:\mathrm{48607}.\mathrm{51}\:=\:\$\:\left({X}\:+\:\mathrm{9551}.\mathrm{85}\right) \\ $$$$\Rightarrow\:{X}\:=\:\$\:\mathrm{39055}.\mathrm{65} \\ $$

Commented by Joel578 last updated on 17/Apr/20

i^((2)) = 0.06 v = (1 + (i^((2)) /2))^(−1) = (1 + ((0.06)/2))^(−1) = (1.03)^(−1)

$${i}^{\left(\mathrm{2}\right)} \:=\:\mathrm{0}.\mathrm{06} \\ $$$${v}\:=\:\left(\mathrm{1}\:+\:\frac{{i}^{\left(\mathrm{2}\right)} }{\mathrm{2}}\right)^{−\mathrm{1}} \:=\:\left(\mathrm{1}\:+\:\frac{\mathrm{0}.\mathrm{06}}{\mathrm{2}}\right)^{−\mathrm{1}} \:=\:\left(\mathrm{1}.\mathrm{03}\right)^{−\mathrm{1}} \\ $$

Commented by pete last updated on 18/Apr/20

thanks very much sir Joel. But please what does P, V_1 , V_2 and v stand for?

$$\mathrm{thanks}\:\mathrm{very}\:\mathrm{much}\:\mathrm{sir}\:\mathrm{Joel}. \\ $$$$\mathrm{But}\:\mathrm{please}\:\mathrm{what}\:\mathrm{does}\:\mathrm{P},\:\mathrm{V}_{\mathrm{1}} ,\:\mathrm{V}_{\mathrm{2}} \:\mathrm{and}\:\mathrm{v}\:\mathrm{stand} \\ $$$$\mathrm{for}? \\ $$

Commented by Joel578 last updated on 19/Apr/20

PV is present value (the value of money right now) In order to determine the upfront amnout now, we should know what is the value of $ 48000 and $ 11300 if they are given right now. v is discount factor = (1 + i)^(−1) Let′s say you deposits $K on a bank, which give you effective annual interest rate i. Then, after n years from now, your deposit is $K(1+i)^n → Future Value (FV) If you know the Future Value, then you can find its Present Value (= $K) PV = FV v^n = $K(1+i)^n . (1+i)^(−n) = $K

$${PV}\:\mathrm{is}\:\mathrm{present}\:\mathrm{value}\:\left(\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{money}\:\mathrm{right}\:\mathrm{now}\right) \\ $$$$\mathrm{In}\:\mathrm{order}\:\mathrm{to}\:\mathrm{determine}\:\mathrm{the}\:\mathrm{upfront}\:\mathrm{amnout}\:{now}, \\ $$$$\mathrm{we}\:\mathrm{should}\:\mathrm{know}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\$\:\mathrm{48000}\:\mathrm{and}\: \\ $$$$\$\:\mathrm{11300}\:\mathrm{if}\:\mathrm{they}\:\mathrm{are}\:\mathrm{given}\:{right}\:{now}. \\ $$$$ \\ $$$${v}\:\mathrm{is}\:\mathrm{discount}\:\mathrm{factor}\:=\:\left(\mathrm{1}\:+\:{i}\right)^{−\mathrm{1}} \\ $$$$\mathrm{Let}'\mathrm{s}\:\mathrm{say}\:\mathrm{you}\:\mathrm{deposits}\:\${K}\:\mathrm{on}\:\mathrm{a}\:\mathrm{bank},\:\mathrm{which}\:\mathrm{give}\:\mathrm{you} \\ $$$$\mathrm{effective}\:\mathrm{annual}\:\mathrm{interest}\:\mathrm{rate}\:{i}.\:\mathrm{Then},\:\mathrm{after}\:{n}\:\mathrm{years}\:\mathrm{from}\:{now}, \\ $$$$\mathrm{your}\:\mathrm{deposit}\:\mathrm{is}\:\${K}\left(\mathrm{1}+{i}\right)^{{n}} \:\rightarrow\:{Future}\:{Value}\:\left({FV}\right) \\ $$$$ \\ $$$$\mathrm{If}\:\mathrm{you}\:\mathrm{know}\:\mathrm{the}\:\mathrm{Future}\:\mathrm{Value},\:\mathrm{then}\:\mathrm{you}\:\mathrm{can}\:\mathrm{find} \\ $$$$\mathrm{its}\:\mathrm{Present}\:\mathrm{Value}\:\left(=\:\${K}\right) \\ $$$$\mathrm{P}{V}\:=\:{FV}\:\:{v}^{{n}} \:=\:\${K}\left(\mathrm{1}+{i}\right)^{{n}} \:.\:\left(\mathrm{1}+{i}\right)^{−{n}} \:=\:\${K} \\ $$

Commented by pete last updated on 25/Apr/20

may you continually increase in knowledge as you continue to give help, Sir

$$\mathrm{may}\:\mathrm{you}\:\mathrm{continually}\:\mathrm{increase}\:\mathrm{in}\:\mathrm{knowledge} \\ $$$$\mathrm{as}\:\mathrm{you}\:\mathrm{continue}\:\mathrm{to}\:\mathrm{give}\:\mathrm{help},\:\mathrm{Sir} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com