Annette Michaelson will need $11,000 in 8 years to help pay for her education. Determine the lump sum, deposited today at 4.5% compounded monthly, will produce the necessary amount.
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
A=11,000
t=8 years
n=12
r=4.5%=0.045
substitute in the formula above
[tex]\begin{gathered} 11,000=P(1+\frac{0.045}{12})^{(12\cdot8)} \\ 11,000=P(\frac{12.045}{12})^{(96)} \\ \\ P=7,679.61 \end{gathered}[/tex]therefore
the answer is
