Compound Interest Sample Problems

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Here are some tips for Compound Interest, which aligns with New York state standards:

Compound Interest

In this topic, we use the same terms as the terms for simple interest.
To review the terms for simple interest, see here.

Compound interest is based on the original principle plus the amount of interest earned in the past.
Simple interest is only based on the original principle.

To calculate how much money you will have at the end of a specific period of time (called the ending balance), use this formula:

Ending Balance = Principle × (1 + Rate)^Time

To calculate how much compound interest you earned,

Compound Interest = Ending Balance - Staring Balance (or Principle)

Example 1:

Answer the following questions involving compound interest. Input all answers to the nearest dollar

Interest Rate: 6% monthly
Starting Balance: $189
Time Passed: 10 months
How much interest has accrued if calculated as compound interest?
What is the new total balance?

Interest:
Total balance:

Calculate the ending balance first.
Then use the compound interest formula to find the amount of interest earned.

Ending balance = Principle × (1 + Rate)^Time

= $189 × (1 + 6% per month)^{10 months}

= $189 × (1.06)¹⁰

= $338.47

Compound Interest = Ending Balance - Principle

= $338.47 - $189

= $149.47

Rounding to the nearest dollar, the answer is Interest: Total balance:

Ending balance	=	Principle × (1 + Rate)^Time
	=	$189 × (1 + 6% per month)^{10 months}
	=	$189 × (1.06)¹⁰
	=	$338.47

Compound Interest	=	Ending Balance - Principle
	=	$338.47 - $189
	=	$149.47