Answer:
11% compounded daily
Step-by-step explanation:
Simple interest is:
A = P (1 + r/n)^(nt)
where A is the final amount,
P is the initial amount,
r is the annual rate,
n is the number of compoundings per year (in this case, 365),
and t is the number of years.
A = 13,000 (1 + 0.11/365)^(365×1)
A = 14,511.37
Continuously compounded interest is:
A = Pe^(rt)
A = 13,000 e^(0.1086×1)
A = 14,491.31
Answer: 11% compounded daily would yield a larger amount in 1 year.
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1 + r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = $13,000
r = 11% = 11/100 = 0.11
n = 365 because it was compounded 365 times in a year.
t = 1 year
Therefore,
A = 13000(1 + 0.11/365)^365 × 1
A = 13000(1 + 0.0003)^365
A = 13000(1.0003)^365
A = $14504.1
The formula for continuously compounded interest is
A = P x e(r x t)
From the information given,
P = $13000
r = 10.86% = 10.86/100 = 0.1086
t = 10
year
Therefore,
A = 13000 x e(0.1086 x 1)
A = 13000 x e(0.1086)
A = $14491.3
