Question

How much would you need to deposit in an account now in order to have $2000 in the account in 5 years? Assume the account earns 6% interest compounded quarterly. Round your answer to the nearest cent.

Answer 1

$1484.94

EXPLANATION :

The compounding formula is :

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

where A = future value

P = present value

r = rate of interest

n = number of compounding

t = time in years

From the problem,

P = unknown

A = $2000

r = 6% or 0.06

n = 4 (Quarterly)

t = 5 years

Using the formula above :

`\begin{gathered} 2000=P\left(1+(0.06)/(4)\right)^(4\left(5\right)) \\ 2000=P\left(1.015\right)^(20) \\ P=(2000)/(1.015^(20)) \\ P=1484.94 \end{gathered}`

The answer rounded to the nearest cent is $1484.94