Question

You deposit $400 into an account that pays 2% annual interest compounded quarterly.
Part a: Write an exponential model that describes the situation.
Part b: Determine the value of the account after 5 years. Round to two decimal places.

Answer 1

Part A
Write an exponential model that describes the situation.
Y (x)=400 (1+0.02/4)^4x
Y the value of the account after x years
400 is the initial deposite
0.02 interest rate
4 compounding periods (quarterly)
X time ( number of years )
Y (x)=400 (1.005)^4x

Part B
Y (5)=400×(1.005)^(4×5)=441.96

Hope it helps!

Answer 2

The exponential model that describes the situation is $400 x 1.05^20.

The value of the account after 5 years would be $441.96.

What is the future value of the account?

Exponential functions usually have this form: ab^x

Where:

• a = initial value
• b = rate of increase
• x = number of years

The formula that can be used to determine the future value of the account is :

FV = P(1+r)^nm

Where:

• FV = Future value
• P = present value
• r = interest rate = 2%/4 = 0.50%
• n = number of years = 5
• m = number of compounding = 4

$400 x 1.05^20 = $441.96

To learn more about exponential functions, please check: https://brainly.com/question/26331578

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