Question

A business has a savings account that earns a 3% annual interest rate. At the end of 1996, the business had $4,000 in the account. Thetformula FPC 1+T100is used to determine the amount in the savings account.• Fis the final amount,• p is the initial investment amount,• r is the annual interest rate, and• t is the time years.To the nearest dollar, how much did the business initially invest in 1991?

Answer 1

Answer:

The amount they initially invest in 1991 is;

$\text{ \ 3,450}$

Explanation:

Given the expression;

$F=p(1+\frac{r}{100})^t$

Where;

F= final amount

p=initial investment

r= annual interest rate

t=time in years

Given that;

The amount in the account in 1996 is $4,000, annual interest rate at 3% ;

$\begin{gathered} F=\text{ \ 4000} \\ r=3\text{\%} \\ t=1996-1991=5\text{ years} \end{gathered}$

Making p the subject of formula;

$\begin{gathered} F=p(1+\frac{r}{100})^t \\ p=\frac{F}{(1+\frac{r}{100})^t} \end{gathered}$

substituting the values;

$\begin{gathered} p=\frac{\text{ \ 4000}}{(1+\frac{3}{100})^{5^{}}} \\ p=\text{ \ 3,450} \end{gathered}$

Therefore, the amount they initially invest in 1991 is;

$\text{ \ 3,450}$