Suppose that when your friend was born, your friend's parents deposited $7000 in an account paying 3.4% interest compounded quarterly. What will the account balance be after 19 years?
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Part 1
The balance after 19 years will be $
enter your response here.
(Round to the nearest cent as needed.)
To calculate the balance after 19 years with quarterly compounding, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (balance)
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
Given:
P = $7000
r = 3.4% = 0.034 (as a decimal)
n = 4 (quarterly compounding)
t = 19 years
Plugging these values into the formula, we get:
A = $7000(1 + 0.034/4)^(4*19)
A ≈ $7000(1.0085)^(76)
A ≈ $7000(2.29885195)
A ≈ $16,091.96
Therefore, the account balance will be approximately $16,091.96 after 19 years.