230k views
0 votes
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.)

User Keran
by
4.1k points

1 Answer

4 votes

Answer:

The answers are:

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

b. Jim will receive $76 as a bonus

Step-by-step explanation:

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


F=P*e^(rt)

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


F=P*e^(rt)


F=6000*1.05654 = 6,339.24

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)

User Irshu
by
4.5k points