Question

A specific type of financial instrument pays 15% simple interest (based on the purchase value) and lasts for 1.5 years. The instrument can be bought at any price. An investor purchases the instrument for P0, and has calculated that the total value of the investment (i.e. P0 plus interest earned) will be $4,000 at maturity. Calculate P0, giving your answer to the nearest dollar. Give your answer in dollars to the nearest dollar. Do not include the dollar symbol or commas in your answer.

Answer 1

3265

Explanation

The simple interest formula is given by

$I=\text{PRT}$

where

I is the interest

P is the principal

R is the rate ( in decimals)

and the is the time

then, let

Rate=15% =0.15

time = 1.5 years

Principal =P

$\begin{gathered} totalvalue=Interest+P=4000 \\ I+P=4000\rightarrow equañtion\text{ (1)} \end{gathered}$

replace the formula into the equation (1)

$\begin{gathered} I+P=4000\rightarrow equañtion\text{ (1)} \\ PRT+P=4000 \\ \text{factorize P} \\ P(RT+1)=4000 \\ \text{divide both sides by (RT}+1) \\ \frac{P(RT+1)}{(Rt+1)}=\frac{4000}{(RT+1)} \\ P=\frac{4000}{(RT+1)} \\ \text{replace R and T values} \\ P=\frac{4000}{(0.15\cdot1.5+1)} \\ P=\frac{4000}{1.225} \\ P=3265.30 \\ rounded\text{ }tot\text{ the nearest dollar} \\ P=3265 \end{gathered}$

therefore , the answer is

3265

I hope this helps you