Finn deposited $3,500 in a new account at his bank.
The bank pays 5.5% interest compounded annually on this account.
Finn makes no additional deposits or withdrawals.
Which amount is closest to the balance of the account at the end of 3 years?
Responses
A $4,109.84$4,109.84
B $192.50$192.50
C $577.50$577.50
D $609.84$609.84
To find the balance of the account at the end of 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial deposit)
r = the interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, Finn deposited $3,500, the interest rate is 5.5% or 0.055 as a decimal, interest is compounded annually (n = 1), and the time is 3 years.
Plugging in the values into the formula, we get:
A = 3500(1 + 0.055/1)^(1*3)
A = 3500(1 + 0.055)^3
A = 3500(1.055)^3
A ≈ 3500(1.169)
A ≈ $4,109.84
So, the closest balance to the account at the end of 3 years is $4,109.84.
Therefore, the correct response is A) $4,109.84.