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

Commented by pete last updated on 17/Apr/20

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

Answered by Joel578 last updated on 17/Apr/20

$$\mathrm{First}\mathrm{option}$$$${PV}_1=48000v^6+11300v^{10}=\mathrm{\$}48607.51$$$$$$$$\mathrm{Second}\mathrm{option}$$$${PV}_2=X+12100v^8=\mathrm{\$}(X+9551.85)$$$$$$$$\mathrm{Now},$$$${PV}_1={PV}_2$$$$\Rightarrow \mathrm{\$}48607.51=\mathrm{\$}(X+9551.85)$$$$\Rightarrow X=\mathrm{\$}39055.65$$

Commented by Joel578 last updated on 17/Apr/20

$$i^{\left(2\right)}=0.06$$$$v={(1+\frac{i^{\left(2\right)}}{2})}^{-1}={(1+\frac{0.06}{2})}^{-1}={(1.03)}^{-1}$$

Commented by pete last updated on 18/Apr/20

$$\mathrm{thanks}\mathrm{very}\mathrm{much}\mathrm{sir}\mathrm{Joel}.$$$$\mathrm{But}\mathrm{please}\mathrm{what}\mathrm{does}\mathrm{P},{\mathrm{V}}_1,{\mathrm{V}}_2\mathrm{and}\mathrm{v}\mathrm{stand}$$$$\mathrm{for}?$$

Commented by Joel578 last updated on 19/Apr/20

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

Commented by pete last updated on 25/Apr/20

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

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