Question

question 9
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?
$

(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.
submit question

Explanation:

Part (a) - Brittany's Savings

Step1: Recall Simple Interest Formula

The formula for simple interest is $I = P \times r \times t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the time in years. The total savings for Brittany will be the principal plus the total interest earned over 10 years.

First, convert the interest rate to decimal: $r = 17\% = 0.17$. The principal $P = 7000$, and $t = 10$ years.

Step2: Calculate Total Interest

Using the simple interest formula, the total interest earned over 10 years is $I = 7000 \times 0.17 \times 10$.
$$I = 7000 \times 0.17 \times 10 = 7000 \times 1.7 = 11900$$

Step3: Calculate Total Savings

The total savings is the principal plus the total interest: $Total = P + I = 7000 + 11900$.
$$Total = 7000 + 11900 = 18900$$

Step1: Recall Compound Interest Formula

The formula for compound interest is $A = P(1 + r)^t$, where $A$ is the amount of money accumulated after $t$ years, including interest, $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the time in years.

Here, $P = 7000$, $r = 0.17$, and $t = 10$ years.

Step2: Substitute Values into the Formula

Substitute the values into the compound interest formula: $A = 7000(1 + 0.17)^{10}$.

First, calculate $(1 + 0.17) = 1.17$. Then, calculate $1.17^{10}$. Using a calculator, $1.17^{10} \approx 4.806863$.

Step3: Calculate the Amount

Multiply the principal by this value: $A = 7000 \times 4.806863$.
$$A \approx 7000 \times 4.806863 \approx 33648.04$$

Answer:

$\$18900$

Part (b) - Devante's Savings