Question

How much would you need to deposit in an account now in order to have $6,000.00 in the account in 389

days?

Assume the account earns 2-% simple interest.

You would need to deposit_____ in your account now.

Answer 1

$5,851.88

Explanation:

`\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ A = P(1 + rt)$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}`

Given values:

• A = $6000
• r = 2³/₈% = 0.02375
• t = 389 days = ³⁸⁹/₃₆₅ years

Substitute the given values into the formula and solve for P:

`\implies 6000=P\left(1+0.02375 * (389)/(365)\right)`

`\implies P=(6000)/(1+0.02375 * (389)/(365))`

`\implies P=(6000)/(1+0.0253116438...)`

`\implies P=(6000)/(1.0253116438...)`

`\implies P=5851.87931....`

Therefore, you would need to deposit $5,851.88 in your account now.