A finance company has a total of $15 million earmarked for homeowner and auto loans. On the average, homeowner loans have a 10% annual rate of return, whereas auto loans yield a 12% annual rate of return. Management has also stipulated that the total amount of homeowner loans should be greater than or equal to 4 times the total amount of automobile loans. Determine the total amount of loans of each type the company should extend to each category in order to maximize its returns.
A) $12 million in homeowner loans, $3 million in auto loans; optimal returns $1.56 million
B) $3 million in homeowner loans, $12 million in auto loans; optimal returns $1.74 million
C) $12 million in homeowner loans, $3 million in auto loans; optimal returns $1.74 million
D) $3 million in homeowner loans, $12 million in auto loans; optimal returns $1.56 million

Question

Quizplus · Accepted Answer

Given the constraint that homeowner loans must be at least 4 times the amount of auto loans, and the total funds available are $15 million, the optimal allocation to maximize returns under these conditions is $12 million in homeowner loans and $3 million in auto loans. This allocation respects the stipulated ratio and utilizes the total funds available. The returns are calculated as 10% of $12 million plus 12% of $3 million, which equals $1.56 million.

A Finance Company Has a Total of $15 Million Earmarked