Math

QuestionKaren invested \$3000 at 5\% and \$7000 at 4\%. Find total interest after 1 year and overall percent interest.

Studdy Solution

STEP 1

Assumptions1. The amount invested in the certificate of deposit is 3,000.Theinterestrateforthecertificateofdepositis53,000. The interest rate for the certificate of deposit is5%<br />3. The amount invested in corporate bonds is 7,0004. The interest rate for the corporate bonds is4%
5. The time for investment is1 year6. The interest is calculated as a one-time payment, not monthly compounding

STEP 2

First, we need to find the interest earned from the certificate of deposit. We can do this by multiplying the invested amount by the interest rate.
InterestCD=InvestedamountCDtimesInterestrateCDInterest_{CD} = Invested\, amount_{CD} \\times Interest\, rate_{CD}

STEP 3

Now, plug in the given values for the invested amount and interest rate to calculate the interest from the certificate of deposit.
InterestCD=$3,000times5%Interest_{CD} = \$3,000 \\times5\%

STEP 4

Convert the percentage to a decimal value.
%=0.05\% =0.05InterestCD=$3,000times0.05Interest_{CD} = \$3,000 \\times0.05

STEP 5

Calculate the interest amount from the certificate of deposit.
InterestCD=$3,000times0.05=$150Interest_{CD} = \$3,000 \\times0.05 = \$150

STEP 6

Next, we need to find the interest earned from the corporate bonds. We can do this by multiplying the invested amount by the interest rate.
InterestCB=InvestedamountCBtimesInterestrateCBInterest_{CB} = Invested\, amount_{CB} \\times Interest\, rate_{CB}

STEP 7

Now, plug in the given values for the invested amount and interest rate to calculate the interest from the corporate bonds.
InterestCB=$7,000times4%Interest_{CB} = \$7,000 \\times4\%

STEP 8

Convert the percentage to a decimal value.
4%=0.044\% =0.04InterestCB=$7,000times0.04Interest_{CB} = \$7,000 \\times0.04

STEP 9

Calculate the interest amount from the corporate bonds.
InterestCB=$7,000times.04=$280Interest_{CB} = \$7,000 \\times.04 = \$280

STEP 10

Now that we have the interest amounts from both the certificate of deposit and the corporate bonds, we can add these to find the total interest earned.
Totalinterest=InterestCD+InterestCBTotal\, interest = Interest_{CD} + Interest_{CB}

STEP 11

Plug in the values for the interest from the certificate of deposit and the corporate bonds to calculate the total interest.
Totalinterest=$150+$280Total\, interest = \$150 + \$280

STEP 12

Calculate the total interest earned.
Totalinterest=$150+$280=$430Total\, interest = \$150 + \$280 = \$430So, the total interest earned at the end of year is $430.

STEP 13

Next, we need to find the total investment made by Karen. This is the sum of the amount invested in the certificate of deposit and the corporate bonds.
Totalinvestment=InvestedamountCD+InvestedamountCBTotal\, investment = Invested\, amount_{CD} + Invested\, amount_{CB}

STEP 14

Plug in the values for the invested amounts to calculate the total investment.
Totalinvestment=$3,000+$7,000Total\, investment = \$3,000 + \$7,000

STEP 15

Calculate the total investment.
Totalinvestment=$3,000+$7,000=$10,000Total\, investment = \$3,000 + \$7,000 = \$10,000

STEP 16

Now, we can calculate the percent interest for her total investment. This is the total interest divided by the total investment, multiplied by100.
Percentinterest=TotalinterestTotalinvestmenttimes100Percent\, interest = \frac{Total\, interest}{Total\, investment} \\times100

STEP 17

Plug in the values for the total interest and the total investment to calculate the percent interest.
Percentinterest=$430$10,000times100Percent\, interest = \frac{\$430}{\$10,000} \\times100

STEP 18

Calculate the percent interest.
Percentinterest=$430$10,000times100=4.3%Percent\, interest = \frac{\$430}{\$10,000} \\times100 =4.3\%So, the percent interest for her total investment is4.3%.

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