Answer: (a) To find the amount in the account at the end of 1 year, we can use the formula for compound interest:
A = P * (1 + r)^n,
where:
A = the amount after n years,
P = the principal amount (initial deposit),
r = the interest rate per period (in decimal form),
n = the number of periods.
In this case:
P = $8000,
r = 14% = 0.14 (as a decimal),
n = 1 year.
Now, plug the values into the formula:
A = $8000 * (1 + 0.14)^1.
Calculate the amount:
A = $8000 * 1.14 = $9120.
So, the amount in the account at the end of 1 year is $9120.
(b) To find the amount in the account at the end of 2 years, we can again use the compound interest formula:
A = P * (1 + r)^n.
Now, n = 2 years (as we want to find the amount after 2 years), and the principal (P) is the amount we found in part (a), which is $9120.
So, for part (b):
A = $9120 * (1 + 0.14)^2.
Calculate the amount:
A = $9120 * 1.14^2 ≈ $9120 * 1.2996 ≈ $11,184.80.
The amount in the account at the end of 2 years is approximately $11,184.80.