jake put $ 600 in the bank for 4 years at 2.5% interest

a) how much interest will he earn after three years

b) what is the total amount in his bank account at the end of three years

To find the answers to the given questions, we will use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = total amount in the bank account after n years
P = principal amount (initial deposit)
r = annual interest rate (expressed as a decimal)
n = number of times the interest is compounded per year
t = number of years

Given:
P = $600
r = 2.5% = 0.025 (expressed as a decimal)
n = 1 (interest compounded annually)
t = 4 years

a) How much interest will Jake earn after three years?

To find the interest earned after three years, we will subtract the initial deposit from the total amount after three years.

Step 1: Calculate the total amount after four years.
A = 600(1 + 0.025/1)^(1*4)
A = 600(1 + 0.025)^4
A ≈ 600(1.025)^4
A ≈ 600(1.103813)
A ≈ $662.29

Step 2: Calculate the total amount after three years.
To find the amount after three years, we can use the same formula but adjust the time period.
A = 600(1 + 0.025/1)^(1*3)
A = 600(1 + 0.025)^3
A ≈ 600(1.025)^3
A ≈ 600(1.078890625)
A ≈ $647.34

Step 3: Calculate the interest earned after three years.
Interest earned = Total amount after three years - Initial deposit
Interest earned ≈ $647.34 - $600 ≈ $47.34

Therefore, Jake will earn approximately $47.34 in interest after three years.

b) What is the total amount in Jake's bank account at the end of three years?

The total amount in Jake's bank account after three years is approximately $647.34.