Question

Simple interest I in dollars is calculated using the formula I=​prt, where p represents the​ principal, or amount in dollars that is invested or​ borrowed; r represents the annual interest​ rate, expressed as a​ decimal; and t represents​ time, in years. Find the value of the variable​ t, using the simple interest formula.
I=$540, p=$4800, r=4.5

Write the interest rate r as a decimal.

r = ?

Answer 1

and we do this one the same way as the other.

$\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&\ 540\\ P=\textit{original amount deposited}\dotfill & \ 4800\\ r=rate\to 4.5\%\to \frac{4.5}{100}\dotfill &0.045\\ t=years \end{cases} \\\\\\ 540=(4800)(0.045)t\implies \cfrac{540}{(4800)(0.045)}=t\implies 2.5=t$

Answer 2

Answer:

$t=2.5$

Step-by-step explanation:

We have been given the formula to simple interest. We are asked to find the variable t using the given formula and given values.

Simple interest formula: $I=Prt$, where,

$I$ = Amount of interest after t years,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

Given: $I=\ 540$, $P=\ 4800$, $r=4.5$

Let us convert our given interest rate in decimal form.

$r=4.5\%=\frac{4.5}{100}=0.045$

Upon substituting our given values in simple interest formula, we will get:

$\ 540=\ 4800\cdot 0.045t$

$\ 540=\ 216t$

$\frac{\ 540}{\ 216}=\frac{\ 216t}{\ 216}$

$2.5=t$

Therefore, the value of t is 2.5 years.