Leona bought a 1-year, $10,000 certificate of deposit that paid intere

Question

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

(A) $10,464
(B) $ 864
(C) $ 816
(D) $ 800
(E) $ 480

Bunuel · Accepted Answer

Approach #1: 8 percent compounded semiannually --> 4% in 6 months. For the first 6 months, interest was 4% of $10,000, so $400; For the next 6 months, interest was 4% of $10,000, plus 4% earned on the previous interest of $400, so $400+$16=$416; Total interest for 1 year was $400+$416=$816. Answer: C. Approach #2: If the interest were compounded annually instead of semiannually , then in a year the interest would be 8% of $10,000, so $800. Now, since the interest is compounded semiannually, there would be interest earned on interest (a very small amount) thus the actual interest should be a little bit more than $800, only answer choice C fits. Answer: C. Similar questions to practice: https://gmatclub.com/forum/john-deposit ... 35825.html https://gmatclub.com/forum/on-the-first ... 28825.html https://gmatclub.com/forum/marcus-depos ... 28395.html https://gmatclub.com/forum/jolene-enter ... 27308.html https://gmatclub.com/forum/alex-deposit ... 26459.html https://gmatclub.com/forum/michelle-dep ... 38273.html Theory: https://gmatclub.com/forum/math-number- ... 91708.html Hope it helps.

lchen · Answer

The equation for compound interest is:
 P_t = P_0(1+\frac{i}{n})^{nt} 
 P_t  is the Principle at time t
 P_0  is the Principle at time 0
 i  is the Interest Rate
 n  is the Number of compounding periods
 t  is the Number of years the investment earns interest

Plug in the numbers:
 P_t = 10,000(1+\frac{.08}{2})^{2*1}

P_t = 10,000(1+\frac{8}{200})^{2}

P_t = 10,000(\frac{200}{200}+\frac{8}{200})^{2}

P_t = 10,000(\frac{208}{200})^{2}

P_t = 10,000(\frac{104}{100})^{2}

P_t = 10,000(\frac{10,816}{10,000})

P_t = 10,816

P_t - P_0= 10,816 - 10,000 = 816

Answer is C

Definitely a more difficult solution, but I know some people really like formulas.

Bunuel · Answer

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Percent and Interest Problems: math-number-theory-percents-91708.html

All DS Percent and Interest Problems to practice: search.php?search_id=tag&tag_id=33
All PS Percent and Interest Problems to practice: search.php?search_id=tag&tag_id=54

yodeepak · Answer

This problem can be solved using formula. However, the calculation in formula is difficult = 10,000(208/200)^2.

The main motive of GMAT behind Compound interest problem is to consume your time so that you waste your precious time in difficult calculations. We have to avoid that trap and use simple and fast calculations.

By definition Compound interest = S.I. + Interest on Interest

So here C.I. = 4% on 10,000 (6months) + 4% on 10,000(6months) + 4% on interest (last 6 months interest)

= 400 + 400 + 4*400/100
 = 400 + 400 + 16 = 816

samirchaudhary · Answer

The amount increases in two steps : 4% in the first 6 months and again 4% in the second 6 months.

Such % change in two steps is knows as successive % change.

In case of successive % change, we can use the below formula to calculate the Net % change :

Net % change =   A + B + \frac{AB}{100}

If there is % increase , we take the value as positive and for % decrease, we take that as negative.

In the final answer, positive number shows % increase and negative number shows % decrease.

Using the above formula , we get : net change =  4 + 4 + \frac{4*4}{100}   = 8 + .16 = 8.16 % .

8.16 % of 10,000  is 816. Hence the answer is 816.

This formula is applicable only in case of % change in two steps. In case % change takes place in 3 steps, we have to apply the formula for the first two first and then to the result and the third one.

EMPOWERgmatRichC · Answer

Hi All,

Interest rate questions are a relatively rare category on Test Day - you'll likely see just one question on the subject and it will involve one or both of the following formulas:

Simple Interest = Principal x (1 + RT)

Compound Interest = Principal x (1 + R)^T

...where R is the yearly interest rate and T is the number of years.

Normally, a question gives you the relevant information to work with, then asks you to perform the calculation. Sometimes there are "twists" though (eg. you're given the end result and have to "work backwards" to find the interest rate or principal) and in rare cases, you'll be asked to deal with a situation in which interest is compounded MORE than once per year.

The 'rule' for handling the Compound Interest Formula in this situation is pretty simple though:

For the number of times that you compound per year:
1) MULTIPLY T by that number
2) DIVIDE R by that number

For example, in this question we have $10,000 at 8% interest compounded SEMI-ANNUALLY (meaning twice per year) for 1 year.

IF...we were just calculating ONCE per year, we'd have......$10,000 x (1 + .08)^1

For TWICE per year (which is what we have here)...............$10,000 x (1 + .04)^2

For FOUR times per year....................................................$10,000 x (1 + .02)^4

For EIGHT times per year...................................................$10,000 x (1 + .01)^8
Etc.

As has been pointed out, the correct answer is  C .

It's important to note the specific wording and numbers in these types of questions. It's common for one (or more) of the wrong answers to be the result of a DIFFERENT/INCORRECT calculation, so if you make a silly mistake, then you won't know that you are wrong.

GMAT assassins aren't born, they're made,
Rich

KarishmaB · Answer

Compound interest is different from simple interest in only one aspect - CI is earned on interest too.
Annual Rate of interest = 8%
Semi annual rate of interest = 4% (because interest is compounded semi annually)

In the first half of the year, interest earned is 4% of 10000 = $400
In the second half of the year, $400 is earned plus interest is earned on the previous $400 i.e. 4% of 400 = $16

Total interest earned = 400 + 400 + 16 = $816

healthjunkie · Answer

For me these problems tend to take more time than necessary because of the more computation that's involved. What I've found to be helpful is an estimation trick that helps you narrow down the choices very quickly and often requires me to do no computation. To Karishma's point, we earn interest on interest when we compound which generally ends up being just over what it would be if it was simple interest. For example the way I would think about it in this problem is...

8% of 10,000= 800. So my answer must be right over 800 which lets me pick C right away without doing any math really. If you're unsure between B & C you can always take the extra step that Karishma did and figure out that if you would earn 800 in the full year at simple interest, than you would earn 400 in the first half of the year and then the extra interest you earn is 4% of 400=16.

Thought I'd throw this approach out there for anyone who hates computing (1.04)^2 as much as i do!

ScottTargetTestPrep · Answer

We use the compound interest equation:

Future Value = (Present Value)(1 + r/n)^nt

where r is the annual interest rate, n is the number of compounding periods per year and t is the amount of time (in years) until maturity.

So we know:

Present Value = 10,000

r = 8% = 0.08

n = 2

t = 1

So we have:

FV = 10,000(1+0.08/2)^(2)(1)

FV = 10,000(1+0.04)^2

FV = 10,000(1.04)(1.04)

FV = 10,000(1.0816) = $10,816

Thus, the amount of interest earned is $10,816 – $10,000 = $816.

We could have also looked at this problem a bit more conceptually. We know that when an investment has a rate of 8% ANNUAL interest and it compounds SEMI-ANNUALLY (twice a year), the investment earns 4% interest every SIX MONTHS. So in this case we know:

Interest earned for the first six months = 0.04 x $10,000 = $400

Her investment is now worth ($400 + $10,000) = $10,400

Interest earned for the next six months = 0.04 x $10,400 = $416

Thus, the total interest earned = $400 + $416 = $816

Answer is C

Divyadisha · Answer

Compound interest= P (1+r/100n)^n

10,000 (1+8/200)^2

10,000 * 104/100 *104/100

Units digit will be 6. Only option C has units digit of 6

AvinashK94 · Answer

P = 10000
R = 8% ( Compounded semiannually, so 4% for 6 months)
N = 2 ( Semi-Annually)

A = 10000 (1 + 4/100) ^2 => 10816
CI = A-P => 10816 - 10000 = 816

Option (C)

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

Leona bought a 1-year, $10,000 certificate of deposit that paid intere

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Leona bought a 1-year, $10,000 certificate of deposit that paid intere

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards