Suppose you deposit $2100 into an account that earns 9% interest, compounded quarterly. Compute the amount of money in the account after 16 years.
$
How much of that is interest?
$
To calculate the amount of money in the account after 16 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount of money in the account after 16 years
P = the principal amount (initial deposit) = $2100
r = the annual interest rate (as a decimal) = 9% = 0.09
n = the number of times the interest is compounded per year = 4 (quarterly)
t = the number of years = 16
Plugging in these values into the formula:
A = 2100(1 + 0.09/4)^(4*16)
A = 2100(1 + 0.0225)^(64)
A ≈ 2100(1.0225)^(64)
A ≈ 2100(2.55704506334445)
A ≈ $5360.79
Therefore, the amount of money in the account after 16 years is approximately $5360.79.
To calculate the amount of interest earned, we subtract the initial deposit from the total amount:
Interest = A - P
Interest = 5360.79 - 2100
Interest ≈ $3260.79
Therefore, the amount of interest earned is approximately $3260.79.