Word problem

Question

A credit card company charges compound interest annually on any unpaid debts at 5%. Mr. Johnson has an outstanding debit on his credit card of $4200. What will be his outstanding debt 3 years from now?

Answer 1

David, our formula is A = P(1 + r/n)^nt

 

A is the amount. P is the principal. r is the rate of interest. t is the time in years. n is the number of times per year interest is compounding.

 

This formula comes from the fact that the compounding is done on top of the new amount each time. If we start with $100, then $5 is added the first year. The second year is 5% of $105, etc.

 

Remember that if we want the price of something at the store with 8% tax, we can multiply the price by .08 and add that to the price. Or, we can multiply the price by 1.08 to get the total with tax.

 

So, at year one, we have, using the $100 example, $100(1.05) = $105. Year 2 is $105(1.05) = $100(1.05)(1.05) = $110.25. Year 3 is $110.25(1.05) = 100(1.05)(1.05)(1.05) = $115.76.

 

If interest is compounded more often than yearly, the interest rate is divided by that many times a year. If you have 5% compounded monthly, then each month is 5/12%. 12 x 5/12 = 5, so you get the full percentage over the year.

 

Back to our formula.

 

A = 4200(1 + .05)³ = $4862.03

 

Hope this helps!

Answer 2

A = p(1 + r/n)^nt, where A= amount, p = principal, r = rate, t = time (years), n = times per year calculated

 

A = 4200(1 + 0.05)³

A = 4200(1.05)³

A ≈ 4200(1.157)

A ≈ 4862.03

 

The balance shall be $4,862.03.