Problem Solving

Leona bought a 1-year, $10,000 certificate of deposit
that paid interest at an annual rate of 8 percent
compounded semiannually. What was the total amount
of interest paid on this certificate at maturity?
(A) $10,464
(B) $ 864
(C) $ 816
(D) $ 800
(E) $ 480

I know this is an easy problem. But the confusion for me lies in this question and the formula given in the BTG flash cards for compound interest problems. It says in the flashcards that for this type of problems: Divide interest by # of times compounded in 1 year to find interest for the compound period.

So, 800/2=400 ???

Gurpinder wrote:Leona bought a 1-year, $10,000 certificate of deposit
that paid interest at an annual rate of 8 percent
compounded semiannually. What was the total amount
of interest paid on this certificate at maturity?
(A) $10,464
(B) $ 864
(C) $ 816
(D) $ 800
(E) $ 480

I know this is an easy problem. But the confusion for me lies in this question and the formula given in the BTG flash cards for compound interest problems. It says in the flashcards that for this type of problems: Divide interest by # of times compounded in 1 year to find interest for the compound period.

So, 800/2=400 ???

It is not actually 800/2, it is 8/2
P(1+r/100)^n
10000(1+4/100)^2
=10000(1.04)^2
=10000(1.0816)
=10816
Hence interest = 10816-10000 = 816

Hope this helps!!

I guess its just best to memorize the formula for this one

Thanks kvcpk!

Gurpinder wrote:I guess its just best to memorize the formula for this one

Thanks kvcpk!

Compounded interest is simple interest plus a little more. Thus, the quickest way to solve this problem is to calculate 8% simple interest and look for an answer choice that is just a bit larger.

8% simple interest = .08*10000 = 800.

The correct answer is C, which is just a bit larger.

Gurpinder wrote:Leona bought a 1-year, $10,000 certificate of deposit
that paid interest at an annual rate of 8 percent
compounded semiannually. What was the total amount
of interest paid on this certificate at maturity?
(A) $10,464
(B) $ 864
(C) $ 816
(D) $ 800
(E) $ 480

I know this is an easy problem. But the confusion for me lies in this question and the formula given in the BTG flash cards for compound interest problems. It says in the flashcards that for this type of problems: Divide interest by # of times compounded in 1 year to find interest for the compound period.

So, 800/2=400 ???

Rather than memorizing a formal, which you may forget or mess up on the test, try this.

Since it's compounded semi annually, you know interest is paid at 6 months, and then you earn interest on the principle AND interest over the next 6 months. If it were quarterly, it would be 4 times. Also, make sure you divide the annual rate by how many times it's being compounded (8/2 for this, 8/4 for quarterly).

So, calculate the first 6 months, $10,000 x .04 = interest of $400. Add it back to the principal since the interest is being compounded for the next 6 months. so, interest for the next 6 months would be $10,400 x .04 = $416. Your total after 1 year would then be 10,816, or 816 interest earned.

Obviously the equation is easier, but it's also easier to mess up.