Question

How much would you need to deposit in an account now in order to have $6000 in the account in 10years? Assume the account earns 3% interest compounded quarterly. Round your answer to thenearest cent.Submit Question

Answer 1

$4450.05

Explanations:

The formula for calculating the compound ammount is expressed as:

`A=P(1+(r)/(n))^(nt)`

Given the following parameters

• Amount after 10 years A = $6000

,

• P is the amount deposited

,

• r is the rate = 3% = 0.03

,

• t is the time t = 10 years

,

• n = 4 (compounding time)

Substitute the given parameters

`\begin{gathered} 6000=P(1+(0.03)/(4))^(4(10)) \\ 6000=P(1.0075)^(40) \\ 6000=P(1.3483) \end{gathered}`

Divide both sides by 1.3483

`\begin{gathered} P=(6000)/(1.3483) \\ P=\$4450.05 \end{gathered}`

Hence the amount you need to deposit now is $4450.05