An investment of $13,000.00 with Barnes Bank earns a 2.36% APR compounded monthly. a. Write a function fthat determines the investment's valuc (in dollars) in terms of the number of years t since the investment was made j(t)-|13,000(1+1.0236/12)"(12t] # Preview b. Determine the investment's value after 20 years Preview c. Determine how long it wil take for the investment's value to double. (Hint: it might be casiest to solve this graphically.)

a. Write a function that determines the investment's value (in dollars) in terms of the number of years t since the investment was made:  13,000 * (1 + 0.0236/12)^(12t) = 13,000 * 1.001967^12t

b. The investment's value after 20 years: $20,833.58

c. How long it will take for the investment's value to double: 352.8 months or 29.4 years.

Explanation:

a. As the interest rate is 2.36% APR compounded monthly, the monthly interest rate is 2.36%/12 and the Effective annual rate of is ( 1 + 0.0236/12)^12 - 1

=> After t years of investment, the value of the account is decided by the function: Interest receipt + Initial investment =  Initial investment * [ ( 1 + 0.0236/12)^(12t) - 1 ] + Initial investment = Initial investment *  1.001967^12t = 13,000 * 1.001967^12t

b. Apply the function above, we have: The investment's value after 20 years = 13,000 * 1.001967^12*20 = 20,833.58

c. The investment's value is double means: 1.001967^12t = 2 <=> 12t = 352.8

<=> t = 29.4 => it will take for the investment's value to double: 352.8 months or 29.4 years.