Sophia invests $6,100 in a retirement account with a fixed annual interest rate of 3% compounded monthly. What will the account balance be after 12 years?

FV= $8,739.38

Step-by-step explanation:

Giving the following information:

Initial investment (PV)= $6,100

Number of periods (n)= 12*12= 144

Interest rate (i)= 0.03/12= 0.0025

To calculate the future value (FV), we need to use the following formula:

FV= PV*(1 + i)^n

FV= 6,100*(1.0025^144)

FV= $8,739.38

just sum

10 + 10 = 20

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)