Question

7.

Find the present value.
Amount Needed: $42,000
Time (Years): 8
Rate: 3%
Compounded: semiannually


$37,283.82

$36,960.00

$33,097.26

$33,155.22

Answer 1

To solve this we are going to use the formula for a 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

Since the amount needed is $42,000,
`FV=42000`. We also know for our problem that
`t=8` and
`r= (3)/(100) =0.03`. Since the interest is compounded semiannually, it is compounded two times per year; therefore,
`n=2`. Lets replace those values in our formula and solve for
`PV`:

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

`42000=PV(1+ (0.03)/(2))^((2)(8))`

`PV= (42000)/((1+ (0.03)/(2))^((2)(8)))`

`PV=33097.30`

We can conclude that the present value needed to make $42000 after 8 years according to your given choices is $33,097.26