Question

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?

Answer 1

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

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