Sharon has $500 to use as an initial investment in a savings account or a cd account. the savings account pays 2.3% simple interest each year. the cd pays 1.8% annual interest compounded monthly.

write a function (model) that would give you the future value of the savings account in any number of years (use t for the unknown number of years).

write a function (model) that would give you the future value of the cd account in any number of years (use t for the unknown number of years). find the future value of both accounts in 20 years. which account should she choose?

Saving account: A = 500(1 + 0.023t)

CD account: A = 500(1 + 0.018/12)^(12t)

Future value of saving account is $730

Future value of CD account is $716.47

She should choose the saving account

Step-by-step explanation:

* Lets revise the rules of simple and compound interest

- Simple Interest Equation (Principal + Interest)

 A = P(1 + rt)

- Where:

•A = Total amount (principal + interest)  future amount

•P = Principal Amount

•I = Interest Amount

•r = Rate of Interest per year in decimal; r = R/100

•t = Time Period involved  

- Compound interest can be calculated using the formula

 A = P (1 + r/n)^(nt)

Where:

•A = the future value of the investment, including interest

•P = the principal investment amount (the initial amount)

•r = the annual interest rate (decimal)

•n = the number of times that interest is compounded per unit t

•t = the time the money is invested for

* Now lets solve the problem

- Saving account:

# P = $500

# r = 2.3/100 = 0.023

# t = t

∴ A = 500(1 + 0.023t) ⇒ (1)

- CD account:

# P = $500

# r = 1.8/100 = 0.018

# n = 12

# t = t

∴ A = 500(1 + 0.018/12)^(12t) ⇒ (2)

* In case t = 20 years

- In equation (1)

# A = 500(1 + 0.023 × 20) = $730

- In equation (2)

# A = 500(1 + 0.018/12)^(12 × 20) = $716.47

* The future value of saving account is greater than the CD account

∴ She should choose the saving account