Question

A bank features a savings account that has an annual percentage rate of $r = 3\%$ with interest compounded quarterly. Kendrick deposits $12,000 into the account. The account balance can be modeled by the exponential formula $A(t) = a(1 + \frac{r}{k})^{kt}$, 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 = $ $r = $ $k = $ (B) How much money will Kendrick have in the account in 9 years? Answer = $\$$ 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.

          A bank features a savings account that has an annual percentage rate of $r = 3\%$ with interest compounded quarterly. Kendrick deposits $12,000 into the account.
The account balance can be modeled by the exponential formula $A(t) = a(1 + \frac{r}{k})^{kt}$, 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 = $
$r = $
$k = $
(B) How much money will Kendrick have in the account in 9 years?
Answer = $\$$
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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a bank features a savings account that has an annual percentage rate of r 3 with interest compounded quarterly kendrick deposits 12000 into the account the account balance can be modeled by 13809

Added by Devin J.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

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Solved by Expert Supreeta N

03/10/2023

Step 1

03$ (annual percentage rate, converted to decimal) $k = 4$ (compounded quarterly) Show more…

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A bank features a savings account that has an annual percentage rate of $r = 3\%$ with interest compounded quarterly. Kendrick deposits $12,000 into the account. The account balance can be modeled by the exponential formula $A(t) = a(1 + \frac{r}{k})^{kt}$, 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 = $ $r = $ $k = $ (B) How much money will Kendrick have in the account in 9 years? Answer = $\$$ 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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00:01 Hi, from the question given that a bank feature to saving account as an annual percentage rate r is equal to 5 .3 % with an interest compounded quarterly.

00:16 Therefore, n is equal to 4.

00:20 So, or here it is mentioned as k.

00:23 So k is equal to 4 and nick deposit $10 ,000 into an account.

00:29 So principal amount, that is the deposited amount is $1 ,000, $10 ,000.

00:35 So the account balance can be modeled by the exponential formula.

00:40 A of t is equal to a times of 1 plus r by k, the old power kt.

00:48 Here a is the account value after t years and small a represents a principal amount.

00:55 So this is small a and r is the rate of annual percentage rate and k is the number of times each year the interest is compounded.

01:04 So, in part a, the value of a is equal to 10 ,000 and r is equal to 5 .3 divided by 100, which is equal to 0 .053 and k is equal to 4.

01:22 Now, let us move on to part b.

01:25 So, in part b, we need to calculate how much money will nick in the account after 9 years.

01:31 So here, t is equal to 9 years.

01:36 So by using the account formula, so we have a is equal to small a is 10 ,000 times 1 plus r is 0 .053 divided by k is 4 the old power k is 4 times t is 9.

01:52 So simplify this...

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