**Interest and investment problems :**

Problems on interest and investment usually involve simple interest using the formula given below.

**I = PRT**

Here,

I = Interest on the original investment

R = Interest rate (Expressed in decimal form)

T = Time ( Expressed in years)

**Example 1 : **

David invests $500 for two years at the interest rate 10%. How much interest will he earn ?

**Solution : **

**Step 1 : **

The interest formula is

I = PRT

Here,

P = 500

R = 10% or 10/100 or 0.1

T = 2 years

**Step 2 : **

Plug the values of P, R and T in the interest formula.

I = 500 x 0.1 x 2

I = 100

Hence, he will earn $100 as interest.

**Example 2 : **

Alex invested $500 and received $650 after three years. What had been the interest rate ?

**Solution : **

**Step 1 :**

Interest earned = A - P

Interest earned = 650 - 500 = 150

And also,

P = 500

T = 3 years

**Step 2 : **

The interest formula is

I = PRT

Plug the values of I, P and T in the interest formula.

150 = 500 x R x 3

150 = 1500 x R

Divide both sides by 1500

150 / 1500 = R

0.1 = R

To convert decimal into percentage, multiply by 100.

(0.1 x 100) % = R

10 % = R

Hence, the interest rate is 10%.

**Example 3 : **

Arthur invests his inheritance of $24000 in two different accounts which pays 6% and 5% annual interest. After one year, he received $1340 in interest. How much did he invest in each account ?

**Solution : **

**Step 1 :**

Let "x" be the money invested at 6% rate.

Then, the money invested at 5% rate = 24000 - x

**Step 2 : **

The interest formula is

I = PRT

**Step 3 : **

Interest earned at 6% rate is

I = (x)(0.06)(1)

I = 0.06x

**Step 4 : **

Interest earned at 5% rate is

I = (24000 - x)(0.05)(1)

I = (24000 - x)(0.05)

I = 1200 - 0.05x

**Step 5 : **

Adding the results of step 3 and step 4, we get

0.06x + 1200 - 0.05x = Total interest

0.01x + 1200 = Total interest

In the question, the total interest is given $1340.

Then, we have

0.01x + 1200 = $1340

**Step 6 : **

Solve for "x"

0.01x + 1200 = $1340

Subtract 1200 from both sides

0.01x = $140

Divide both sides by 0.01

x = 140 / 0.01

**x = 14000**

Then,

24000 - x = 24000 - 14000

**24000 - x = 10000 **

Hence, the money invested at 6% rate is $14000 and 5% rate is $10000.

**Example 4 : **

Josh invested some money at 6% annual interest and three times as much at 8%. The total interest after one year was $660. How much did he invest at each rate ?

**Solution : **

**Step 1 :**

Let "x" be the money invested at 6% rate.

Then, the money invested at 8% rate = 3x

**Step 2 : **

The interest formula is

I = PRT

**Step 3 :**

Interest earned at 6% rate is

I = (x)(0.06)(1)

I = 0.06x

**Step 4 : **

Interest earned at 8% rate is

I = (3x)(0.08)(1)

I = 0.24x

**Step 5 : **

Adding the results of step 4 and step 5, we get

0.06x + 0.24x = Total interest

0.3x = Total interest

In the question, the total interest is given $660.

Then, we have

0.3x = $660

**Step 6 :**

Solve for "x"

0.3x = $660

Divide both sides by 0.3.

x = 660 / 0.3

**x = 2200**

Then,

3x = 3(2200)

**3x = 6600 **

Hence, the money invested at 6% rate is $2200 and 8% rate is $6600.

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