Question

Find the price of the house in 2015, information and details are in the image provided.!

Answer 1

Answer:

$A=\text{ \ }476,798.01$

Explanation: A house was purchased in 1950, since then the price of the house has been increasing at a compounded rate of 5% each year, we want to know the price of the house in 2015.

The original price was:

$\text{ \ 20,000}$

We know that the compound interest can be calculated with the following formula:

$A=P(1+\frac{r}{n})^{nt}$

Where each of the variables has the following meaning:

$\begin{gathered} A=\text{ Final amount} \\ P=\text{ Principle amount or initial amount} \\ r=\text{ interest rate} \\ n=\text{ Number of times compounded per time period} \\ t=\text{ Number of time periods} \end{gathered}$

Therefore the information needed to use this formula is (all that is given in the question);

$\begin{gathered} P=\text{ \ 20,000} \\ r=\text{ 5\% =}\frac{5}{100}=\text{ 0.05} \\ t=\text{ 2015-1950=}65 \\ n=1 \end{gathered}$

Substituting in the formula gives:

$\begin{gathered} A=20,000(1+\frac{0.05}{1})^{(1\times65)}=20,000(1.05)^{65}=20,000\times(23.84)=\text{ \ }476,798.01 \\ \therefore\rightarrow \\ A=\text{ \ }476,798.01 \end{gathered}$

Note! The difference in price in 1950 and 2015, is huge, this teaches us the difference between compound and simple interest!