Question

if you receive a 175.84 cents on 314 invested at a rate of 7% for how long did yo invest the principle

Answer 1

The number of years you should invest the principal is;

`8\text{ years}`

Step-by-step explanation:

Given;

`\begin{gathered} \text{Interest i = \$175.84} \\ \text{ Principal P = \$}314 \\ \text{Rate r = 7\% =0.07} \end{gathered}`

Recall that the formula for simple interest is;

`\begin{gathered} i=P* r* t \\ t=(i)/(Pr) \\ \text{where;} \\ t=\text{time of investment} \end{gathered}`

substituting the given values;

`\begin{gathered} t=(i)/(Pr) \\ t=(175.84)/(314*0.07) \\ t=(175.84)/(21.98) \\ t=8 \end{gathered}`

Therefore, the number of years you should invest the principal is;

`8\text{ years}`

We can also solve as;

`\begin{gathered} i=P* r* t \\ 175.84=314*0.07* t \\ 175.84=21.98t \end{gathered}`

then we can divide both sides by 21.98;

`\begin{gathered} (175.84)/(21.97)=(21.98t)/(21.98) \\ 8=t \\ t=8\text{ years} \end{gathered}`