Brody deposited $500 into an account that
earns 4.2% interest compounded annually. He
makes no additional deposits and no withdrawals.
Approximately how much interest will the account
have earned after 7 years?
A 167
B 420
C 542
D 665
The answer is A but I need help with the actual equation. like I need the equation to this.
500(1.042^7 - 1)
value = 500 (1 + .042)^7
interest = value - 500
To find the amount of interest earned after 7 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount including the interest
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case:
P = $500
r = 4.2% = 0.042 (decimal form)
n = 1 (compounded annually)
t = 7
Plugging in these values into the formula, we get:
A = 500(1 + 0.042/1)^(1*7)
A = 500(1 + 0.042)^7
A ≈ $668.15
To find the amount of interest earned, we subtract the initial deposit from the final amount:
Interest = A - P
Interest ≈ $668.15 - $500
Interest ≈ $168.15
Rounding to the nearest whole number, the approximate amount of interest earned after 7 years is $167, which corresponds to option A.