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

The amount they initially invest in 1991 is;

`\text{ \$3,450}`

Step-by-step explanation:

Given the expression;

`F=p(1+(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+(r)/(100))^t \\ p=(F)/((1+(r)/(100))^t) \end{gathered}`

substituting the values;

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

Therefore, the amount they initially invest in 1991 is;

`\text{ \$3,450}`