Banking and Lending Rates

Question

Wendy, a loan officer, has $1,000,000 to lend is required to obtain an average of 18% per year. If she can lend at the rate of 19% or 16%, how much can she lend at the 16% and still meet her requirement?

Answer 1

Assume that he lends amount 'x' at 16%. 

=> Amount lend at 19% = 1,000,000 - x 

 

He wants to obtain average of 18% per year, i.e, 0.18* (1,000,000)   -Eqn (1)

Amount obtained from lending at different rates = Amount obtained from 16% + Amount obtained at 19%

 = 0.16 * x + 0.19 * (1,000,000 -x)    -Eqn(2)

 

By (1) and (2),   => 0.18* (1,000,000) = 0.16 * x + 0.19 * (1,000,000 -x)

 

=> 0.03 x = 0.01 * (1,000,000)

=> x= 333,333.33 $  

 

 

ALTERNATE:    Assume a see- saw as :              16-------18---19

where, 18 is the balance and 16 and 19 are two ends. 

Total weight at 16 and 19 is 1,000,000. 

Assuming 'x' at 16, weight at 19 would be '1,000,000 -x'. 

So by weight law, (Weight at 16) * Distance of 16 from center balance = (Weight at 19) * Distance of 19 from center balance

=> x* (18-16) = (1,000,000-x) * (19-18)

which yields the same equation

 

Hope this help.

Cheers !