Dominic pays 9% interest on his $22000 college loan and 11% interest on his $16000 car loan. What average interest rate does he pay on the total
$38000 he owes? Round your answer to the nearest tenth of a percent.
Elvi/la -- please use the same name for your posts.
Find the interest he pays on his 9% loan
Find the interest he pays on the 11% loan
Add them up for a total of T
avg rate = T/(22000 + 16000) * 100%
To find the average interest rate Dominic pays on the total $38000 he owes, we need to calculate the weighted average of the interest rates on his college loan and car loan based on the amounts owed.
Step 1: Calculate the total interest paid on the college loan:
Total interest paid on college loan = Principal * Rate = $22000 * 9% = $1980
Step 2: Calculate the total interest paid on the car loan:
Total interest paid on car loan = Principal * Rate = $16000 * 11% = $1760
Step 3: Calculate the total interest paid on both loans:
Total interest paid = Total interest on college loan + Total interest on car loan = $1980 + $1760 = $3740
Step 4: Calculate the total amount owed:
Total owed = College loan amount + Car loan amount = $22000 + $16000 = $38000
Step 5: Calculate the average interest rate:
Average interest rate = (Total interest paid / Total owed) * 100 = ($3740 / $38000) * 100 ≈ 9.8%
Therefore, Dominic pays an average interest rate of 9.8% on his total $38000 debt.
To find the average interest rate Dominic pays on the total amount he owes, we need to compute the weighted average of the two interest rates.
The weighted average formula is as follows:
Average Interest Rate = (Amount 1 * Interest Rate 1 + Amount 2 * Interest Rate 2) / Total Amount
First, we calculate the interest for each loan:
Interest on college loan = $22,000 * 9% = $1,980
Interest on car loan = $16,000 * 11% = $1,760
Next, we find the total amount Dominic owes:
Total Amount = College loan + Car loan = $22,000 + $16,000 = $38,000
Now, we substitute the values into the formula:
Average Interest Rate = ($1,980 + $1,760) / $38,000
Simplifying the expression:
Average Interest Rate = $3,740 / $38,000
Calculating the division:
Average Interest Rate ≈ 0.0984
To convert the decimal to a percentage:
Average Interest Rate ≈ 9.84%
Therefore, the average interest rate Dominic pays on the total $38,000 he owes is approximately 9.84%.