Question

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

Answer 1

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