Question

$4700 accumulating to $5994.76, compounded monthly for 5 years. What is the interest rate %

Answer 1

48.76%

Explanation:

Compound interest describes interest on the principal plus interest.

Compound Interest Formula

The formula to find compound interest is
`A=P(1+(r)/(n))^(nt)`. In the formula:

• A is the total amount,
• P is the principal,
• r is the rate as a decimal,
• n is how often interest is compounded,
• t is time.

We can plug in our information to find the rate.

Solving For Interest Rate

First, let's rewrite the equation with our information. Note that for simplicity I will write rounded values for each step, but in reality, no rounding should be done until the last step.

• 
  `5994.76 = 4700(1+(r)/(12))^(12*5)`

Then, simplify the exponent and divide both sides by 4700.

• 
  `1.275=(1+(r)/(12) )^(60)`

Take the 60th root of both sides.

• 
  `1.004=(1+(r)/(12) )`

Subtract 1 from both sides.

• 
  `0.004063=(r)/(12)`

Finally, multiply both sides by 12.

• r = 0.04876

This means that the rate is 0.04876. We can multiply this by 100 to get the rate as a percentage. The interest rate is 48.76%.