Total money that will be in the account in 10 years = 45000
Time period = 10 years
Rate of interest = 5% or 0.05
n = 12 (number o times the money is compounded)
Let the principal (p) be = x
Formula for compound interest = [tex]A=p(1+\frac{r}{n})^{nt}[/tex]
Putting the values in the formula we get,
[tex]45000=x(1+\frac{0.05}{12})^{10*12}[/tex]
[tex]45000=x(\frac{12+0.05}{12})^{120}[/tex]
[tex]45000=x(1.004)^{120}[/tex]
[tex]45000=1.614x[/tex]
[tex]x=27881.04[/tex]
Hence, the principle amount should be approximately $27881.
