Question

A finance company has a total of $20 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 that Madison should extend to each category in order to maximize its returns. housing million dollars automobile million dollars

Answer 1

Housing million dollars $1,655.2

Automobile million dollars $413.80

Step-by-step explanation:

Calculation to determine the total amount of loans of each type

Calculation for HOMEOWNER LOANS

Homeowner loans=$20,000-[(10%*20,000)/(4*12%+10%)]*10%

Homeowner loans=[$20,000-($2,000/48%+10%)]*10%

Homeowner loans=[$20,000-($2,000/58%)]*10%

Homeowner loans=[$20,000-$3,448.3]*10%

Homeowner loans=$16,552*10%

Homeowner loans=$1,655.2

Calculation for AUTO LOANS

Auto Loans=[(10%*20,000)/(4*12%+10%)]*12%

Auto Loans=($2,000/(48%+10%)]*12%

Auto Loans=($2,000/58%)*12%

Auto Loans= $3,448.3*12%

Auto Loans=$413.80

Based on the above calculation Homeowner loans amount of $1,655.2 is 4 times Auto Loans amount of $413.80

Therefore the total amount of loans of each type that Madison should extend to each category in order to maximize its returns are:

Housing million dollars $1,655.2

Automobile million dollars $413.80