 Quandaries and Queries

Hello, my name is Kat and I am not a student at this time.

If I have three debts and 49% percent of total debt is  loaned at 9% intrest, 34% of the debt is at 21%  intrest and 17% of the total debt is at 14% intrest, how do I calculate the average rate of intrest on total debt? I just can seem to figure this one out. I need average percent of intrest rates for a program I am using to map out a pay down plan. thank you so much for any reply. (and yes I know I should pay down high intrest first! :) )

Hi Kat,

Suppose that your total debt was \$100 and calculate how much interest you would owe in one year.

debt number Amount Interest
1 \$49 9% of \$49 = 0.09 \$49 = \$4.41
2 \$34 21% of \$34 = 0.21 \$34 = \$7.14
3 \$17 14% of \$17 = 0.14 \$17 = \$2.38
Total \$100 \$13.93

Thus on \$100 you owe an interest of \$13.93 and hence the interest rate is

\$13.93/\$100 = 0.1393 or 13.93%

Suppose now that you total debt was \$K rather than \$100. What changes? The debts are

49% of \$K = 0.49 K
34% of \$K = 0.34 K
17% of \$K = 0.17 K

Thus I get

debt number Amount Interest
1 \$(0.49 K) 9% of \$(0.49 K) = 0.09 0.49 K = 0.0441 K
2 \$(0.34 K) 21% of \$(0.34 K) = 0.21 0.34 K = 0.0714 K
3 \$(0.17 K) 14% of \$(0.17 K) = 0.14 0.17 K = 0.0238 K
Total \$K 0.1393 K

Thus on \$K you owe an interest of \$0.1393 K and hence the interest rate is

0.1393 K/\$K = 0.1393 or 13.93%

Penny

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