an investment yields an annual interest of $1500. If $500 more is invested and the rate is 2% less, the annual interest is $1300. What is the amount of investment and the rate of interest?

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- Sep 6th 2010, 02:19 PMaeroflixan investment
an investment yields an annual interest of $1500. If $500 more is invested and the rate is 2% less, the annual interest is $1300. What is the amount of investment and the rate of interest?

- Sep 6th 2010, 02:40 PMpickslides
Sounds like a job for some simultaneous equations.

Given A is the initial amount invested, r is the rate then

Maybe use

(1+r)A= 1500+A ...(1)

and

(A+500)(1+(r-2))=1300+(A+500) ...(2)

Leaves you with some algebra.

I may be over complicating this one, it is early morning here! - Sep 6th 2010, 02:45 PMSoroban
Hello, aeroflix!

Quote:

An investment yields an annual interest of $1500.

If $500 more is invested and the rate is 2% less, the annual interest is $1300.

What is the amount of investment and the rate of interest?

Let $\displaystyle x$ = amount invested.

Let $\displaystyle r$ = rate of interest.

We are told that $\displaystyle x$ dollars at $\displaystyle r$ percent yields $1500.

. . Equation: .$\displaystyle rx \:=\:1500$

We are told that $\displaystyle (x+500)$ dollars at $\displaystyle (r-0.02)$ percent yields $1300.

. . Equation: .$\displaystyle (x+500)(r-0.02) \:=\:1300 $

Now solve the system of equations.

You will get a quadratic equation

and must discard one of the roots. - Sep 8th 2010, 12:20 AMaeroflix
thanks