Question

Simple Interest?

You have been given $20 000 from your parents to place in two different investments (Silicon World and Solar Energy). Silicon World offers an annual interest rate of 10% and Solar Energy offers a 6% annual interest rate. Together the investments return a total of $1800 at the end of the year. Determine the amount of money placed in each investment. Justify your answer?

Answer 1

Amount of money placed in Silicon world = `$15000`
and Amount of money placed in Solar Energy = `$5000`

Explanation:

Given: $20 000

Place in two different investments (Silicon World and Solar Energy).

Let the amount placed in Silicon world be `x`

Silicon World offers an annual interest rate of 10%

So the interest on this amount will be given by:

`SI_1 = (PRT)/100 = (x xx10 xx 1)/100 = 0.1x`

where, P is principal amount invested
R is rate of interest, and
T is duration of investment which is given to be 1 year.

Now the amount invested in Solar Energy will be `20000 -x`
It offers a 6% annual interest rate, so the simple interest at the end of 1 year on this will be:

`SI_2 = (PRT)/100 = ((20000-x ) xx 6 xx 1 )/100`

`SI_2 = (120000 - 6x)/100`

Given that: together the investments return a total of $1800 at the end of the year.

`=> SI_1 + SI_2 = 1800`

`=> 0.1x +(120000 - 6x)/100 = 1800`

`=> 10x +120000 - 6x = 180000`

`=> 4x = 180000-120000 = 60000`

`=> x = 15000`

`therefore` Amount of money placed in investment Silicon world is `$15000`
and Amount of money placed in Solar Energy was $20000-15000 = $5000#

Cross heck:

1 : Silicon world: Amount invested: $15000 at rate 10% for 1 year will return interest: `$15000 xx 10 /100xx 1 = $1500`
and
2: Solar energy : amount invested : $5000 at rate of 6% for 1 year will return interest : `$5000 xx 6/100 xx 1 = $300`

Total returns from 1 and 2 : `$1500 + $300 = $ 1800`