The formula for compound interest is given by:
[tex]A=P(1+\frac{r}{n}) ^{nt}[/tex]
where,
A=amount,
P=principal
r=rate of interest
t=time(years)
n=number of times the interest is compounded annually.
Now we are given,
A=amount = 47,500
P=principal= 600
r=rate of interest= 8% or 0.08
n= 4 ( quarterly)
t=time(years)= is to be found
Plugging these in the formula,
[tex]47500=600(1+\frac{0.08}{4}) ^{4t}[/tex]
[tex]47500=600(1.02) ^{4t}[/tex]
[tex]79.167=(1.02) ^{4t}[/tex]
On solving, we get
t=55.19 years
Answer: It will take 55.19 years for $600 to amount to $47,500.
