SOLUTION: Patrick is a loan officer at a bank. He has $2,000,000 to lend out and has two loan programs. His home equity loan is currently priced at 6% per annum, and his unsecured personal l

Question 1093159: Patrick is a loan officer at a bank. He has $2,000,000 to lend out and has two loan programs. His home equity loan is currently priced at 6% per annum, and his unsecured personal loan is priced at 14%. The bank president wants Patrick to earn a rate of return of 12% on the $2,000,000 available. How much should Patrick lend out at 6%?
Found 2 solutions by richwmiller, greenestamps:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
Patrick should follow his conscience and quit since the bank is gauging the customers.
otherwise
.06h+.14u=.12*2000000
h+u=2000000

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

You can of course solve this problem using some variation of the standard algebraic approach, which was suggested in the first response you got to your question. However, there is a much faster method for solving this kind of "mixture" problem, if you can understand it.

The 12% target return is three-fourths of the way from the 6% of the home equity loan and the 14% of the unsecured personal loan. That means three-fourths of the $2 million should be loaned at the higher rate. So

3/4 of $2 million = $1.5 million for the unsecured personal loan and
1/4 of $2 million = $0.5 million for the home equity loan.
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