One safe investment pays 10% per year , and a more risky investment pays 18% per year. A woman who has $143900 to invest woulld like to have an income of $19670 per year from her investments, how much should she invest at each rate
Answers
Answer:
The woman should invest an amount of $ 77900 at 10% and an amount of $ 66000 at 18%.
Explanation:
Given data:
A woman invests an amount of $143900.
She wants to have an income from the investment of $19670 per year.
Rate of interest for the safe investment is 10%
Rate of interest for the risky investment is 18%
Let “x” be the amount invested at 10% per year and “y” be the amount invested at 18% per year.
According to the question we can write,
x + y = 143900 ….. (i)
and,
10% of x + 18% of y = 19670
Or, 0.1x + 0.18y = 19670 ….. (ii)
Multiplying 0.1 throughout the eq. (i) and then subtracting from eq. (ii), we get
0.1x + 0.18y - 0.1x - 0.1y = 19760 – (143900 * 0.1)
Or, 0.08y = 5280
Or, y = 5280/0.08 = $ 66000
Substituting y = 66000 in eq. (i), we get
x + y = 143900
Or, x = 143900 – 66000 = $ 77900