I have been racking my head with this one and don't know how to approach it.
The question is:
A bank loaned out $64,000, part of it at the rate of 13% per year and the rest at a rate of 5% per year. If the interest received was $6000, how much was loaned at 13%.
I know the formula is I=PrT but i don't seem to be able to apply it to this problem.
Thanks so much for the help!!
.13x + .05(64000-x)=6000
solve for x.
Wrong formula for this.
Let x = amount loaned at 13%.
Then 64,000-x = amt loaned at 5%.
0.05x + 0.13(64,000-x) = 6000
solve for x. I get 35,000 @ 13% (and 29,000 @ 5%).
Check my thinking. Check my work. At the end of the problem, multiply the amount at 13% and the amount at 5%, add the two interests to see that it totals $6,000.
Thank you so much, I feel confident that I can tackle this type of problem now.
0.05x + 0.13(64,000-x) = 6000
this is incorrect..
since you said that x is the amount of money loaned at 13% the equation should be;
0.13x + .05(64000-x)=6000
your answer though is correct
35K @ 13% and 29K @ 5%
To solve this problem, you can set up a system of two equations based on the given information.
Let's denote the amount loaned at 13% as 'x' and the amount loaned at 5% as '64000 - x' (since the total loan amount is $64,000).
Now, let's find the interest earned on each loan separately.
For the loan at 13%, the interest earned is calculated using the formula I = PrT, where 'I' is the interest, 'P' is the principal (amount loaned), 'r' is the rate, and 'T' is the time (in years). In this case, the interest earned on this loan is 0.13x.
For the loan at 5%, the interest earned is 0.05(64000 - x), since the amount loaned at 5% is '64000 - x'.
Since the total interest earned is $6000, we can set up the equation:
0.13x + 0.05(64000 - x) = 6000.
Now, let's solve this equation step by step:
0.13x + 3200 - 0.05x = 6000
0.13x - 0.05x = 6000 - 3200
0.08x = 2800
x = 2800 / 0.08
x = 35000
Therefore, $35,000 was loaned at a rate of 13%.