Answer:
$5750.1
Explanation:
The amount she started with can be referred to as present value (PV), while the amount sum she has after the 7 years is the future value (FV).
Thus:
FV = PV[tex](1 +\frac{r}{m}) ^{nm}[/tex]
From the question, FV = $10000, m = 3, n = 7 and r = 0.08.
10000 = PV[tex](1+\frac{0.08}{3}) ^{(3*7)}[/tex]
= PV[tex](1.0267)^{(21)}[/tex]
= 1.7391PV
PV = [tex]\frac{10000}{1.7391}[/tex]
= 5750.1006
PV = 5750.1
The equivalent amount the she had to start with is $5750.1.
The equivalent amount would be as follows:
$[tex]5750.1[/tex]
Given that,
Present value of the principal = $10,000
Rate of interest = 8%
Time = 7 years
We know that,
The principal was compounded quarterly,
No. of quarters in 7 years = 7 × 3
= 21
So,
The Future Value = Present Value[tex](1 + r/m)^_{nm}[/tex]
⇒ 10,000 = Present Value [tex]( 1 + 0.08/3)^{21}[/tex]
∵ Present Value [tex]= 10,000/1.7391[/tex]
[tex]=[/tex] $[tex]5750.1[/tex]
Thus, $[tex]5750.1[/tex] is the correct answer.
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