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QuestionYolanda deposited \$1000 at 2% and \$3000 at 7%. Find total interest earned in 1 year and percent interest on total.
(a) Total interest: \$\square (b) Percent interest: \%

Studdy Solution

STEP 1

Assumptions1. Yolanda deposited 1000intoanaccountwitha1000 into an account with a% annual interest rate. She also deposited 3000 into an account with a7% annual interest rate3. No withdrawals were made from either account within the year4. The interest is calculated as a one-time payment at the end of the year, not compounded monthly

STEP 2

First, we need to find the interest earned from each account. We can do this by multiplying the deposited amount by the interest rate for each account.
Interest=Deposited amounttimesInterest rateInterest = Deposited\, amount \\times Interest\, rate

STEP 3

Now, plug in the given values for the deposited amount and interest rate to calculate the interest for the first account.
Interest1=$1,000times2%Interest1 = \$1,000 \\times2\%

STEP 4

Convert the percentage to a decimal value.
2%=0.022\% =0.02Interest1=$1,000times0.02Interest1 = \$1,000 \\times0.02

STEP 5

Calculate the interest amount for the first account.
Interest1=$1,000times0.02=$20Interest1 = \$1,000 \\times0.02 = \$20

STEP 6

Repeat the process for the second account.
Interest2=$3,000times%Interest2 = \$3,000 \\times\%

STEP 7

Convert the percentage to a decimal value.
7%=0.077\% =0.07Interest2=$3,000times0.07Interest2 = \$3,000 \\times0.07

STEP 8

Calculate the interest amount for the second account.
Interest2=$3,000times0.07=$210Interest2 = \$3,000 \\times0.07 = \$210

STEP 9

Now that we have the interest amounts for both accounts, we can add them together to find the total interest earned.
Total interest=Interest+Interest2Total\, interest = Interest + Interest2

STEP 10

Plug in the values for the interest from both accounts to calculate the total interest.
Total interest=$20+$210Total\, interest = \$20 + \$210

STEP 11

Calculate the total interest amount.
Total interest=$20+$210=$230Total\, interest = \$20 + \$210 = \$230The total interest earned at the end of year is $230.

STEP 12

To find the percent interest for the total deposited, we first need to find the total amount deposited. This is the sum of the amounts deposited into both accounts.
Total deposited=Amount deposited in account +Amount deposited in account 2Total\, deposited = Amount\, deposited\, in\, account\, + Amount\, deposited\, in\, account\,2

STEP 13

Plug in the values for the amounts deposited into both accounts to calculate the total deposited.
Total deposited=$,000+$3,000Total\, deposited = \$,000 + \$3,000

STEP 14

Calculate the total deposited amount.
Total deposited=$,000+$3,000=$4,000Total\, deposited = \$,000 + \$3,000 = \$4,000

STEP 15

Now that we have the total deposited and the total interest, we can calculate the percent interest for the total deposited. This is the total interest divided by the total deposited, then multiplied by100 to convert it to a percentage.
Percent interest=(Total interest/Total deposited)times100Percent\, interest = (Total\, interest / Total\, deposited) \\times100

STEP 16

Plug in the values for the total interest and the total deposited to calculate the percent interest.
Percent interest=($230/$4,000)times100Percent\, interest = (\$230 / \$4,000) \\times100

STEP 17

Calculate the percent interest.
Percent interest=($230/$4,000)times100=5.75%Percent\, interest = (\$230 / \$4,000) \\times100 =5.75\%The percent interest for the total deposited is5.75%.

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