Solve the problem.
-A loan officer at a bank has $97,000 to lend and is required to obtain an average return of 12% per year. Ifhe can lend at the rate of 13% or the rate of 11%, how much can he lend at the 11% rate and still meet hisrequired return?

Question

Quizplus · Accepted Answer

Let x be the amount of money the loan officer can lend at 13% and y be the amount of money he can lend at 11%. We can set up a system of equations to represent the given information:

x + y = $97,000 (total amount lent)
0.13x + 0.11y = 0.12($97,000) (required average return)

Simplifying the second equation, we get:

0.13x + 0.11y = $11,640

Multiplying both sides by 100 to eliminate the decimals, we get:

13x + 11y = $1,164,000

Now we can use substitution to solve for y:

x + y = $97,000
x = $97,000 - y

Substituting into the equation above, we get:

13($97,000 - y) + 11y = $1,164,000

Simplifying and solving for y, we get:

$1,261,000 - 2y = $1,164,000
$97,000 = 2y
y = $48,500

Therefore, the loan officer can lend $48,500 at 11% and still meet his required return of 12%. Let's assume the loan officer lends $x at 13% and $(97,000-x) at 11%.

The annual return from lending $x at 13% is 0.13x.
The annual return from lending $(97,000-x) at 11% is 0.11(97,000-x).

We know that the overall annual return must be 12%, so:

0.13x + 0.11(97,000-x) = 0.12(97,000)

Simplifying this equation, we get:

0.02x = 1,050

x = $52,500

Therefore, the loan officer can lend $(97,000-$52,500) = $44,500 at 11% and still meet his required return.

So, the answer is A) $48,500.00.

Solve the Problem. -A Loan Officer at a Bank Has $97,000 to Lend