Question

What is the compounded interest after 3 years if you invest $10 000 and earn an interest rate of 5% per year?

Step 1: Find the interest for the first year
Step 2: Add the interest to the original amount
Step 3: Determine interest on the new total

Answer 1

Compound Interest is the interest that is compounded on a particular sum of money or investment over a given period of time.

• The interest for the first year is $1,576.25
• The sum of money after adding the original to the interest is $11,576.25
• The interest on the new total is $13,400.96

• Step 1: Find the interest for the first year.

The formula is given as:

A = P(1 + r/n)^nt

P = Principal = $10,000

R = Rate = 5%

n = 1

t = 1

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 10,000(1 + 0.05/1)^(1)(3)

A = 10,000.00(1 + 0.05)^(3)

A = $11,576.25

I = A - P

Hence:

I = $11,576.25 - $10,000.00

I (interest) = $1,576.25

• Step 2: Add the interest to the original amount.

$10,000 +  $1,576.25

= $11,576.25

• Step 3: Determine interest in the new total

The formula is given as:

A = P(1 + r/n)^nt

P = Principal = $11,576.25

r = 0.05 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 11,576.25(1 + 0.05/1)^(1)(3)

A = 11,576.25(1 + 0.05)^(3)

A = $13,400.96

Therefore,

• The interest for the first year is $1,576.25
• The sum of money after adding the original to the interest is $11,576.25
• The interest on the new total is $13,400.96

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