Question

6.

Find the present value.
Amount Needed: $12,300
Time (Years): 4
Rate: 4%
Compounded: quarterly


$10,514.04

$11,820.05

$10,332.00

$10,489.69

Answer 1

To solve this we are going to use the formula for future value:
`FV=PV(1+ (r)/(n) )^(nt)`
where

`FV` is the future value

`PV` is the present value

`r` is the interest rate in decimal form

`n` is the number of times the interest is compounded per year

`t` is the time in years

We know for our problem that
`FV=12300`,
`r= (4)/(100) =0.04`, and
`t=4`. Since the interest is compounded quarterly, it is compounded 4 times per year; therefore,
`n=4`. Lets replace those values in our formula to find and solve for
`PV`:

`FV=PV(1+ (r)/(n) )^(nt)`

`12300=PV(1+ (0.04)/(4) )^((4)(4))`

`PV= (12300)/((1+ (0.04)/(4) )^((4)(4)) )`

`PV=10489.70`

We can conclude that the present amount needed to have $12,300 after 4 years according to your given choices is $10,489.69