Respuesta :
The answer is C) 14 years.
Plug it in to check:
12500(1+0.0525)^14
12500(2.05) = 25,587.01 (rounded to 25000)
Plug it in to check:
12500(1+0.0525)^14
12500(2.05) = 25,587.01 (rounded to 25000)
Answer:
14 years
Step-by-step explanation:
Principal = $12,500
Rate = 5.35%
Amount = $25,000
Now we are supposed to find the time
Formula : [tex]A =P(1+\frac{r}{n})^{nt}[/tex]
Where A = amount = $25,000
P = principal = $12,500
r = rate of interest in decimal = 0.0525
n = no. of compounds per year = 1
Substitute the values :
[tex]25000 =12500(1+\frac{0.0525}{1})^{t}[/tex]
[tex]25000 =12500(1.0525)^{t}[/tex]
[tex]\frac{25000}{12500} =(1.0525)^{t}[/tex]
[tex]2=(1.0525)^{t}[/tex]
Taking log both sides
[tex]\log 2 = t \log(1.0525)[/tex]
[tex]\frac{\log 2}{\log 1.0525} = t [/tex]
[tex]13.5464 = t [/tex]
So, t = 13.5464 years ≈ 14 years
Thus it will take 14 years for the fund to be worth $25,000.
