Problema Solution
Bernhard plans to lend $48000 at simple interest rates of 16% and 19%. How should he allot the loans in order to obtain a return of 18.5%?
Answer provided by our tutors
let
P1 = the money given at r1 = 16% simple interest rate
P2 = the money given at r2 = 19% simple interest rate
P1 + P2 = 48,000
r = %18.5
the simple interest is calculated by the formula
I = Prt
where
P is the principal;
r is the annual interest rate;
t is the time in years.
in our case we have
I1 + I2 = I where
I1 the simple interest on P1
I2 the simple interest on P2
I the simple interest of 18.5% on the total $48,000
P1*r1 + P2*r2 = (P1 + P2)*r
0.16*P1 + 0.19*P2 = 0.185*48000
0.16*P1 + 0.19*P2 = 8800
by solving the system of equations
P1 + P2 = 48000
0.16*P1 + 0.19*P2 = 8800
we find
P1 = $10,666.67
P2 = $37,333.33
Bernhard should lend $10,666.67 at simple interest rate of 16% and $37,333.33 at simple interest rate of 19%.