A financial adviser was showing a client the value, rounded to the

Could anyone help me understand why can we infer it is a compound interest?
Thank you!­

Official answer:

 
We know that \(A = P(1 + r)^n\)

\(130.01 = 100 * (1+r)^5\)
\((1 + r)^5 = 1.3001\)

Now you can simply keep multiplying every previous value with 1.3001 on the calculator.

So Amount after 10 years =\( 130.01 * (1 + r)^{5} = 130.01 * 1.3001 = 169.03\)
This amount is shown as 160.02 so ERROR of $9. 
ANSWER

Amount after 15 years = 169.03 * 1.3001 = 219.75


Amount after 20 years = 219.75 * 1.3001 = 285.70


Amount after 25 years = 285.70 * 1.3001 = 371.43
This amount is shown as 317.43 so ERROR of a bigger amount. Select as Second Error. So select previous error as First Error.
ANSWER

Amount after 30 years = 371.43 * 1.3001 = 482.90


­

mehul2494
ruis
Hi, even if one does not realize initially, the values should be 100, 130.01 and then 160.02 and 190.03 and then 220.04
But you do not have value except 160.02, so either all else are wrong or 160.02 is wrong.
Thus, you could check if it is simple interest by adding 130.01-100 or 30.01 successively to 100.­

 
­chetan2u apart from noticing the values in the answer choices, the information from the question that helps us understand that we are talking about compound interest is the highlighted one?

thanks in advance

­
with the simple interest, we have many answer pairs. We can easily calculate the interest value and projections for coming years which do not match for many values. This can be a hint for trying compound interest. ig

­of course we can move on to the calculations but it is time consuming, so could we consider the statement under the assumption that the value increases by r% per year for some positive constant r as an evidence for the compound interest?

 
We can't right, r is always +ve constant. But about the calcuation part; the calcuation is very easy here, after 1st interest we get 130.01 from 100 so simple interest is 30.01, for other years we can simply add 30.01 we get 160.02, 190.03, 220.04, 250.05, 280.06 we can see there are more than 3 choices for 2 errors.

How do you answer this question in less than a minute?

First, understand the statement clearly.

Then, by using the calculator, as soon as you get that there is a 30% increase every 5 years, use the following prompt: 

after 10 years:   130 x 1.3 = 169 (from the calculator)
after 15 years:  then press "x" "1.3" directly from the result, and you'll get 219
after 20 years:  then press "x" "1.3" directly from the result, and you'll get 285
.....

Until you get the amount in year 30 (less than 15 seconds for all the computations).
After all, compare the incorrect values with the table.

Sometimes, the calculator can be time-consuming; using it smartly can help you make the difference! 

Cheers
Val­

KarishmaB how to do these calculations fast? Even calculator will take time since typing in digital format is wring so how to save time on this

­For every subsequent calculation, you only have to multiply the previous value by 1.3001. You don't need to key in the previous value, it will already be there on your calculator. You simply have to type "x 1.3001" for each subsequent term. It is certainly do-able without wasting much time. 

The value of 20 years have been rounded of to 0.70 instead of 0.69?­

­285.69789 is closer to 285.70 as compared to 285.69, so when rounded off 285.69789 will become 285.70

If it were 285.691 or 285.692 or 285.693 or 285.694, it would be rounded off to 285.69. But 285.695 or bigger number till 285.7049 would be rounded off to 285.70

KarishmaB How did you know that it's compound interest from the question?

One way here could be to eyeball and detect out of place values without any major calculation.

We know after first 5 years return was $130 which means after 10 years it would definitely be greater than $160 via compound interest because if it would have been simple interest than the value would have been $160 (30 x 2) so first value in the options is definitely the incorrect one.

Next detect the gap areas b/w these options every next increment would be greater than previous increment for compound interest. After first 5 years, increment was 30, next 5 would have been let's say b/w 35-40 and so on.

220 - 160 = 60 (We know that 160 is incorrect here and right value should have been definitely greater than 160, so let's reduce this difference a little and assume that right choice would have given a difference of 50)
285 - 220 = 65 (This looks decent from previous diff of 50)
317 - 285 = 32 (Ok this is completely out of place as correct difference here should have been around 80-90 here.)
482 - 317 = 165 (And this justifies the idea, as right value here would have been somewhere around 100-120 from the previous difference which means 317 here is definitely incorrect and quite lower than the actual value)

IMO: (A, D)