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+(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+(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=(65,750)/(4.440213) \\ P=14807.84 \end{gathered}`

Answer: Third choice