[tex]\large{\mathcal{QUESTION:}}[/tex]
What is the present value of Php 185,567.35 due in 5 years and 3 months if money is 7% compound quarterly?
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[tex]\large{\mathcal{SOLUTION:}}[/tex]
Using the formula for present value:
- [tex]\rm{P = F - P(1+\frac{r}{n})^{nt}}[/tex]
[tex] \\ [/tex]
Given:
- F = 185,567.35
- T = 5yrs and 3 months or 5.25
- R = 7% or 0.07
- N = quarterly or 4 times a year
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Solving ,
- [tex]\rm{P = F - P(1+\frac{r}{n})^{nt}}[/tex]
- [tex]\rm{P = 185,567.35 - P(1+\frac{0.07}{4})^{4×5.25}}[/tex]
- [tex]\rm{P = 185,567.35 - P(1+0.0175)^{21}}[/tex]
- [tex]\rm{P = 185,567.35 - P(1.0175)^{21}}[/tex]
- [tex]\rm{P = 185,567.35 - P(1.439536814)}[/tex]
- [tex]\rm{P = 185,567.35 - 1.439536814P}[/tex]
- [tex]\rm{P + 1.439536814P= 185,567.35 }[/tex]
- [tex]\rm{2.439536814P= 185,567.35 }[/tex]
- [tex]\rm{P= 185,567.35 ÷ 2.439536814 }[/tex]
- [tex]\rm{P=76,066.63238}[/tex]
Therefore , the present value is Php 76,066.63
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[tex]\large{\mathcal{ANSWER:}}[/tex]
- the present value is Php 76,066.63
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