Problema Solution
An amount of money invested for 1 year in a savings account will earn $240. That same money, invested in a mini-mall development will earn $1920 interest in a year, because the interest paid is 14 percentage points more than that paid by the savings account. Find the rate of interest paid by each investment.
Answer provided by our tutors
let x = the money invested for 1 year
r1 = the annual rate that earns $240 interest per year
x*r1 = 240 => x = 240/r1
r2 = the annual rate that earns $1920 interest per year
x*r2 = 1920 => x = 1920/r2
now we can write
240/r1 = 1920/r2 multiply both sides by r1*r2
240*r2 = 1920*r1 divide both sides by 240
r2 = 8*r1
the interest paid is 14 percentage points more than that paid by the savings account
r2 = r1 + 0.14
we have the system of equations
r2 = 8*r1
r2 = r1 + 0.14
by solving we find
r1 = 0.02 or 2%
r2 = 0.16 or 16%
click here to see the step by step solution of the system of equations
the interest rate of the saving account is 2%.
the interest rate of the second investment is 16%.