Question

Sasha's bank account earns 4% simple interest. How much must she deposit in the account today if she wants it to be worth $1,000 in 5 years? Round your answer to the nearest dollar.Do NOT round until you have calculated your final answer.

Answer 1

$833

Explanation:

Sasha's bank account earns 4% simple interest. She wants her deposit, P to be worth $1,000 in 5 years.

The formula for the amount in an account at simple interest is given as:

`\begin{gathered} Amount=Principal+Simple\text{ Interest} \\ A(t)=P+(PRT)/(100) \end{gathered}`

From the given information:

• A(t)=$1,000

,

• R=4%

,

• T= 5 years

Substitute these values into the formula:

`1000=P+(P*4*5)/(100)`

Then solve for P:

`\begin{gathered} 1000=(100P+20P)/(100) \\ 1000=(120P)/(100) \\ Multiply\;both\;sides\;by\;(100)/(120) \\ 1000*(100)/(120)=(120P)/(100)*(100)/(120) \\ P\approx\$833.33 \\ P\approx\$833 \end{gathered}`

If Sasha wants her deposit to be worth $1,000 in 5 years, the amount she must deposit is $833 (to the nearest dollar.)