Question

score on last try: 2 of 4 pts. see details for more. at least one scored part is incorrect. jump to first changable incorrect part. get a similar question you can retry this question below brittany started a savings account with simplebank, which pays simple interest. this means that the interest is not put back into the account, but is sent to brittany. the bank has agreed to pay 17% interest, paid annually. brittany deposited $7000 into the account at the beginning of year 1. brittany is going to put the interest each year into a box hidden in their closet. devante also has $7000 to put in a savings account, but decides to go to compbank, which offers compound interest, compounded annually, also at an annual rate of 17%. with compound interest, the interest is put back into the account, and then interest is paid based on the new total in the account. at the end of year 10, assuming each bank is still paying the same interest rate, (a) how much will brittany have in savings in all, both in the bank and in the box? $18900 (b) how much will devante have in savings in all (in the bank)? $ warning: these interest rates are made-up numbers. actual interest rates vary and may be much lower.

Explanation:

Step1: Recall compound interest formula

The formula for compound interest is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the number of years.
Here, $P = 7000$, $r = 0.17$ (since 17% = 0.17), and $t = 10$.

Step2: Substitute values into formula

Substitute $P = 7000$, $r = 0.17$, and $t = 10$ into the formula:
$A = 7000(1 + 0.17)^{10}$

Step3: Calculate $(1 + 0.17)^{10}$

First, calculate $1 + 0.17 = 1.17$. Then, $1.17^{10}\approx 4.806863$.

Step4: Calculate the final amount

Multiply $7000$ by $4.806863$:
$A = 7000\times4.806863\approx 33648.04$

Answer:

$\$33648.04$ (or a more precise value depending on the calculation of $1.17^{10}$, for example, using a calculator for higher precision: $1.17^{10}=1.17\times1.17\times\cdots\times1.17$ (10 times) $\approx 4.806856$ and $7000\times4.806856 = 33647.992\approx 33648.00$ or more decimal places as needed)