Suppose that when your friend was born, your friend's parents deposited $5000 in an account paying 6.9% 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 find the account balance after 19 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the account balance after time t,
P = the principal amount (initial deposit),
r = annual interest rate (in decimal form),
n = number of times interest is compounded per year, and
t = number of years
Given:
P = $5000
r = 6.9% = 0.069 (since r is given as a decimal)
n = 4 (quarterly compounding)
t = 19 years
Plugging in the values into the formula:
A = 5000(1 + 0.069/4)^(4*19)
A = 5000(1 + 0.01725)^(76)
A ≈ $13,684.42 (rounded to the nearest cent)
Therefore, the account balance will be approximately $13,684.42 after 19 years.