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

Answer:

$4450.05

Explanations:

The formula for calculating the compound ammount is expressed as:

$A=P(1+\frac{r}{n})^{nt}$

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

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

Divide both sides by 1.3483

$\begin{gathered} P=\frac{6000}{1.3483} \\ P=\ 4450.05 \end{gathered}$

Hence the amount you need to deposit now is $4450.05