Jim deposits $6,000 into a money market account interest at an annual rate of 5.5% compounded continuously.
(a) Jim's average balance over one year is $ (Use an integer.)
(a) Suppose that at the end of the year the fund pays a bonus that is equal to 1.2% of the average balance. Jim will receive $ as a bonus. (Use an integer.)

The answers are:

a. Jim's average balance over one year is $6339 (using an integer)

b. Jim will receive $76 as a bonus

Explanation:

For the future value of a deposited amount compounded continuously, the formula below is used:

where:

F = Future value

P = present value = $6000

е = Euler's constant = 2.7183

r = interest rate in decimal = 5.5% = 5.5/100 = 0.055

t = time in years = 1 year

∴

Note that  the constant 'e' can be used directly on the calculator

Future value = $6,339 [ to the nearest integer(whole number)]

b. 1.2% of the average balance = 1.2% of 6,339

= 1.2/100 × 6339

= 0.012 × 6339 = $76.07

= $76 ( to the nearest integer)