If &2,000 left in an account for 5 years earned interest of $600, then how much interest would be earned in 6 years.

Question

For a given interest rate, simple interest varies jointly as the principal and time.  

Answer 1

First, let us look at the equation for simple interest:

I=PRT

Where I=interst, P=principal amount, R=interest rate and T=time

 

The problem gives us a principal amount, a time, and an amount of interest that was earned. If we substitute these values into the equation we now have this:

 

600=(2000)R(5)

 

We need to find the interest rate of the given situation in order to tell how much interest would be earned in 6 years. If we simplify this equation we now have:

 

600=10000R

 

Next divide both sides of the equation by 10,000 to get the interest rate (R) alone. We find 

 

600/10000 = R but since interest is usually given as a decimal we have 

0.06 = R

 

We can now use this to substitute back into the simple interest equation with the new data of 6 years. The principal amount does not change and the interest rate must be the same as what we found so we now have this equation:

 

I=(2000)(0.06)(6)

 

If we simplify the right side of the equation we find the earned interest to be:

 

I=720

 

**After six years, this account would earn $720 in interest.

Answer 2

i=prt

$600=$2000*r*5

$600=$10,000*r

600/10,000=r

6/100=r, or 6%(6%=0.06)

i=$2000*0.06*6

i=$2000*0.36

i=$720

If this is simple interest, then if $600 is earned in 5 years, $600/5=$120 interest earned each year.

For six years , 6*$120=$720 interest earned, or $600+$120(one more year's interest)=$720

 

 

Answer 3

Simple interest, I = Prt, P = original Principal, r = rate, t = time.

 

A similar problem is:

 

If $3,000 left in an account for 3 years earned interest of $400, then how much interest would be earned in 5 years?

 

P = $3000, t = 3 yrs, I = $400.

 

$400 = $3000(r)(3 yrs)

 

Divide both sides by $3000(3 yrs):

 

$400/($3000(3 yrs)) = r = 4/90 = 2/45 per year

 

In 5 years:

 

I = $3000((2/45)/year)(5 years)

 

I = $30000/45 = $6000/9 = $2000/3 = (2/3)(1000)

 

2/3 = 0.666666...

 

I = $666.67

Answer 4

1400 ( 1 + r) ^5 = 2000

 

( 1 + r) ^5 = 10/ 7

 

   5 log ( 1 +r) = log 10/7 

 

    log ( 1 +r) = 1/5 log 10/7 

 

    log ( 1 +r) = 0.031

 

    1+ r = 1.073989412

 

  r = 0.074

 

     1400 ( 1 + 0.074) ^6 = 2148 .59