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

Answer:

$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:

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

From the given information:

• A(t)=$1,000

,

• R=4%

,

• T= 5 years

Substitute these values into the formula:

$1000=P+\frac{P\times4\times5}{100}$

Then solve for P:

$\begin{gathered} 1000=\frac{100P+20P}{100} \\ 1000=\frac{120P}{100} \\ Multiply\;both\;sides\;by\;\frac{100}{120} \\ 1000\times\frac{100}{120}=\frac{120P}{100}\times\frac{100}{120} \\ P\approx\ 833.33 \\ P\approx\ 833 \end{gathered}$

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