A bank features a savings account that has an annual percentage rate of
r
=
2.7
% with interest compounded quarterly. Tom deposits $9,000 into the account.
The account balance can be modeled by the exponential formula
A
(
t
)
=
a
(
1
+
r
k
)
k
t
, where
A
is account value after
t years ,
a is the principal (starting amount),
r is the annual percentage rate,
k is the number of times each year that the interest is compounded.
(A) What values should be used for
a , r, and k?
a=9,000
Correct,
r=0.027
Correct,
k=4Correct
(B) How much money will Tom have in the account in
9years?Amount = $
Round answer to the nearest penny.
(C) What is the annual percentage yield (APY) for the savings account? (The APY is the actual or effective annual percentage rate which includes all compounding in the year).
APY= %Round answer to 3 decimal places.
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?
and … your subject is Math.
You didn’t have to imitate them @oobleck that’s very rude.
@oobleck, its vertical cuz sometimes it goes wonky because they copied and pasted,
and @Summer D. HI!
To answer these questions, we can substitute the given values into the exponential formula:
A(t) = a(1 + r/k)^(kt)
(A) Substituting the values,
a = $9,000 (Initial deposit)
r = 0.027 (Annual percentage rate expressed as a decimal)
k = 4 (compounded quarterly)
(B) To find the amount after 9 years, we'll substitute t = 9 into the formula:
A(9) = 9000(1 + 0.027/4)^(4*9)
(C) To find the annual percentage yield (APY), we'll use the formula:
APY = (1 + r/k)^k - 1
Now, let's calculate:
(A) Amount after 9 years:
A(9) = 9000(1 + 0.027/4)^(4*9)
A(9) = 9000(1.00675)^(36)
A(9) ≈ $12,786.31
Therefore, Tom will have approximately $12,786.31 in the account after 9 years.
(B) Annual Percentage Yield (APY):
APY = (1 + 0.027/4)^4 - 1
APY ≈ 0.02718 or 2.718%
Therefore, the annual percentage yield (APY) for the savings account is approximately 2.718%.