Question

What must the rate be less than to be worth it to incur a compensating balance of $1,200 in order to get a 1.5-percent lower interest rate on a 1-year, pure discount loan of $100,000? Select one: a. The rate must be less than 15.58%. b. The rate must be greater than 15.58%. c. The rate must be greater than 19.27%. d. The rate must be less than 19.27%.

Answer 1

We have to calculate is $100,000 x(1+i) is greater or $ 101,200 x (1+[ i-0.015] is greater

Solving the equation below to find out is by incurring compensating balance and getting 1.5% discount is advisable or not

$100,000 x (1+i) > $101,200 x (1+[ i-0.015]

$100,000 / $101200 x (1+i) > (1+[ i-0.015]

0.9881 + 0.9881i > (1+[ i-0.015]

0.9881i – 1i > 1-0.9881-0.015

-0.0119i > -0.0031

i> -0.0031/ -0.0119

i>0.265 or 26.5%

if the interest rate is greater than 26.50% it makes sense in this case the answer is c. The rate must be greater than 19.27%