Question

What is the principal of 65,750 due in 10 years if money us worth 15% compounded monthly?*15,478.41*16,252.39*14,807.84*15,078.97

Answer 1

Compound Interest

The future value (FV) of a principal (P) invested at an annual rate of r compounded m times per year is:

$FV=P\cdot\mleft(1+\frac{r}{m}\mright)^{m\cdot t}$

Where t is the time in years.

The final value is given as FV=65,750 for a t =10 year investment at r = 15% = 0.15 compounded monthly (m=12 times a year).

Substituing:

$65,750=P\cdot\mleft(1+\frac{0.15}{12}\mright)^{12\cdot10}$

Calculating:

$\begin{gathered} 65,750=P\cdot(1.0125)^{120} \\ 65,750=P\cdot4.440213 \end{gathered}$

Solving for P:

$\begin{gathered} P=\frac{65,750}{4.440213} \\ P=14807.84 \end{gathered}$

Answer: Third choice