SOLUTION: How much money should Rita invest 6 2/3% stock at 110 to source an annual income of 900?

Question 854352: How much money should Rita invest 6 2/3% stock at 110 to source an annual income of 900?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
she buys the stock at 110 per share and it will give her 6 2/3 % interest per year is what i think you are asking.

6 2/3 % per year is equal to 20/3 % per year which is equal to an interest rate of 20/300 per year.

if we let x = the number of shares, then the formula becomes:

20/300 * 110 * x = 900

simplify this to get:

1/15 * 110 * x = 900

multiply both sides of this equation by 15 to get:

110 * x = 900 * 15 = 13500

divide both sides of this equation by 110 to get:

x = 13500 / 110

this can be simplified to 1350 / 11 which can't really be simplified any further.

we'll keep it as a fraction to avoid never ending decimals which have to be rounded.

the number of shares is equal to 1350 / 11

let's see if this works.

formula was 20 / 300 * 110 * x = 900

we replace x with 1350 / 11 to get:

20 / 300 * 110 * 1350 / 11 = 900

simplify the left side of this equation to get 900 = 900

this is what we were looking for so the solution is good.

you could also convert everything to decimals and you'll get the same answer or something very close to it depending on whether round intermediate results or not.

let's start again and work it with decimal equivalents rather than fractions.

you pay 110 a share.

x = number of shares.

interest rate is 6 and 2/3 % which is equivalent to 6.6667 % which is equal to .066667 interest rate.

formula becomes:

.066667 * 110 * x = 900

divide both sides of this equation by .066667 * 110 and you get:

x = 900 / (.066667 * 110) = 122.726659

122.726659 shares at 110 apiece cost 13499.93249 dollars.

.066667 * 13499.93249 is equal to 899.9999993

the answer is very close to 900 and would have been exactly equal to 900 if i didn't round intermediate results.

since i was pretty liberal with the number of decimal digits i carried it out to, the answer was extremely close. rounding intermediate results to 1 or 2 decimal digits would have been further away.

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