Respuesta :
Compound Interest
The final value of an investment of P dollars for t years at an interest rate of r is given by:
[tex]FV=P\mleft(1+\frac{r}{m}\mright)^{m\cdot t}[/tex]Where m is the number of compounding periods per year.
(a)
Lori buys a CD for P = $1500 that earns r = 6% = 0.06 interest compounded monthly for t = 10 years. Here m = 12 because there are 12 months in a year.
Substituting:
[tex]\begin{gathered} FV=1500\mleft(1+\frac{0.06}{12}\mright)^{12\cdot10} \\ \text{Calculate:} \\ FV=1500(1.005)^{120} \\ FV=2729.10 \end{gathered}[/tex]The CD will be worth $2729.10 in 10 years.
(b) If the interest compounds daily, then m = 360. Calculating:
[tex]\begin{gathered} FV=1500\mleft(1+\frac{0.06}{360}\mright)^{360\cdot10} \\ FV=1500(1.0001666)^{3600} \\ FV=2733.04 \end{gathered}[/tex]The CD will be worth $2733.04 in 10 years.
(c) For t = 5 years:
[tex]\begin{gathered} FV=1500\mleft(1+\frac{0.06}{360}\mright)^{360\cdot5} \\ FV=1500(1.0001666666)^{1800} \\ FV=2024.74 \end{gathered}[/tex]The CD will be worth $2024.74 in 5 years.
