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.