How much must Sam invest to have $3000 in 4 years at a 7.75% interest rate compounded monthly??

Question

my daughter had this homework tonite and i cant firgure it out
HELP IS DUE TOMMOROW
and show steps plz

Answer 1

The interest rate is 7.75% = 7.75/100 annually.
Since it is compounded monthly, the monthly rate is 7.75/1200.
The interest is compounded 48 times as 4yr is 48 months.
If $x is the amount needed, then:
x (1 + (7.75/1200))^48 = 3000
x = $2202.54.

Answer 2

Amount=principal(1+i)^n

Where
Amount is the final total
principal is the orginal investment
i is the periodic interest rate
n is the number of periods

Given i = 0.0775, Amount = $3000

We will divide the annual interest rate by 12 to convert to monthly rate and multiply the number of years by 12 to convert to months. The interest rate and number of time periods have to be in unison.

$3000 = principal(1+0.0775/12)^(4*12)
principal = $3000 /1+0.0775/12)^(4*12)
principal = $3000 /1.3620668

principal = $2,202.54

.

Answer 3

this is compounded investment question
fv= future value=3000
pv=present value=?
int=0.0775
m=12 (compounded monthly)
yr=4
n=m*yr
=12*4
=48
fv=pv*(1+int)^n
3000=pv*(1+0.0775)^48
3000=pv*(35.9774)
pv=83.39
sam must invest $83.39 now