Answer:
n = 1, this means the interest compounds ANNUALLY.
Step-by-step explanation:
Carlos deposited $7,924 into a savings account 30 years ago. The account has an interest rate of 4.6% and the balance is currently $30,541.83. How often does the interest compound?
Compound Interest Formula
: A = P(1 + r/n)^nt
A = Amount after time t
P = Principal (Initial Amount Invested)
r = Interest rate
n = Number of times the interest is compounded
t = time in years
A = $30,541.83
r = 4.6% = 0.046
t = 30
P = $7,924
Hence,
$30,541.83 = $7924(1 + 0.046/n)^30n
Divide both sides by 7924
$30,541.93/$7924 = (1 + 0.046/n)^30n
$30,541.93/$7924 = (n + 0.046/n)^30n
3.8543576477 = (n + 0.046/n)^30n
We take the logarithm of both sides
log 3.8543576477 = log (n + 0.046/n)^30n
Solving for n,
n = 1
Therefore, from the calculation above, since n = 1, this means the interest compounds ANNUALLY.
