Question

An investment of $3000 is made at an annual simple interest rate of 5%. How much additional money must be invested at an annual simple interest rate of 9% so that the total annual interest earned is 7.5% of the total investment?

Answer 1

Additional money invested is $ 5000.

Explanation:

#Initial investment = $3000
Interest = 5%

Yield from Initial investment = `3000 xx 5/100 = 150`

Additional Investment = x
interest = 9%
Yield from Additional Investment = `x xx 9/100=(9x)/100`

Total Investment ( Initial investment + Yield from Additional Investment) `= 3000+x`

Rate of return from total investment = 7.5%
Yield from Total investment `=(3000+x)7.5/100`

Yield from Total investment = Yield from Initial investment +Yield from Additional Investment

Algebraically -

`(3000+x)7.5/100 = 150 +(9x)/100`
`(22500+7.5x)/100- (9x)/100 = 150` [Multiply both side by 100]
`22500+7.5x- 9x = 15000`
`-1.5x= 15000 -22500`
`x=( -7500)/-1.5=5000`