Question

Pregunta ♀️ 1The balance of an account after t years can be found using the expression 4,500(1.75)^t where the initial balance was $4,500. By what percent does the account increase annually?

Answer 1

Solution:

Given:

$A=4500(1.75)^t\ldots\ldots.\ldots\ldots\ldots.\ldots..\ldots..(1)$

where $4500 is the initial balance.

The balance of an account after t-years represents the amount.

The formula for amount is given by;

$\begin{gathered} A=P(1+r)^t \\ \\ \text{where;} \\ P\text{ is the initial balance} \\ P=4500 \end{gathered}$

Hence,

$A=4500(1+r)^t\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots.\mathrm{\cdot}..(2)$

Comparing equation (1) and equation (2);

$\begin{gathered} 4500(1.75)^t=4500(1+r)^t \\ \\ \text{Hence,} \\ 1.75=1+r \\ 1.75-1=r \\ r=0.75 \\ \\ Since\text{ the rate is measured as a percentage,} \\ r=0.75\times100 \\ r=75\text{ \%} \end{gathered}$

Therefore, the percent (rate) that the account increases annually is 75%