Question

One safe investment pays 10% per year, and a more risky investment pays 18% per year. A woman who has $142,400 to invest would like to have an income of $19,440 per year from her investments. How much should she invest at each rate? 10% $ 18% $

Answer 1

Given data:

A woman invests an amount of $142,400.

She wants to have an income from the investment of $19440 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 = 142400 ….. (i)

and,

10% of x + 18% of y = 19440

Or, 0.1x + 0.18y = 19440 ….. (ii)

Multiplying 0.1 throughout the eq. (i).

0.1x+0.1y=142400*0.1 ....... (iii)

(ii) - (iii), we get

0.1x+0.18y - (0.1x + 0.1y) = 19440 -(142400 * 0.1)

0.1x + 0.18y - 0.1x - 0.1y = 19440 – (142400 * 0.1)

Or, 0.08y = 5200

Or, y = 5200/0.08 = $ 65000

Substituting y = 65000 in eq. (i), we get

x + y = 142400

Or, x = 142400 – 65000 = $ 77400.