If $10,000 is invested at x percent simple annual interest

[Guest]

If $10,000 is invested at x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?

A) 10,000(x^n)
B) 10,000(x/100)^n
C) 10,000n*(x/100)
D) 10,000(1+x/100)^n
E) 10,000n*(1+x/100)

I chose B, but the official answer is C. Any thoughts?

Let's say n=2 and x=10 percent
$10,000 would earn $1,000 in year 1 and $1,100 in year 2 for a total of $2,100.

Plugging these values into C gives us $2,000.

[tlien]

Simple interest means you get the same interest every year (which is simple, hehe). I think the one you calculated was compounded interest.


Please correct me If I am wrong.


Eric

[RonPurewal]

Simple interest means you get the same interest every year (which is simple, hehe). I think the one you calculated was compounded interest.


Please correct me If I am wrong.


Eric

this is correct. simple interest calculates interest based on the original value of the investment, regardless of the amount of interest that the investment has accrued. therefore, the formula becomes just Prt, where P is the original amount of the investment, r is the interest rate (expressed as a decimal), and t is the time (usually in years).
the actual value of the investment after this time, not to be confused with the above formula (which represents only the total interest), is P + Prt = P(1 + rt).

[RonPurewal]

If $10,000 is invested at x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?

A) 10,000(x^n)
B) 10,000(x/100)^n
C) 10,000n*(x/100)
D) 10,000(1+x/100)^n
E) 10,000n*(1+x/100)

I chose B, but the official answer is C. Any thoughts?

Let's say n=2 and x=10 percent
$10,000 would earn $1,000 in year 1 and $1,100 in year 2 for a total of $2,100.

Plugging these values into C gives us $2,000.

as the poster above has commented above, you're thinking about compound interest, not simple interest. two totally different animals; don't confuse them.

by the way, it's interesting (heh, "interest"ing) that you didn't apply your number picking to the choice that you picked. if you plug exactly the same numbers into choice (b), you'll get 10,000(0.10)^2, or $100, an absurdly low value. worse yet, according to that formula, the value of the investment would actually shrink every year, and dramatically at that.

even if you didn't realize that you were using the wrong formula, you could still get this problem right by using number plugging: with your n = 2 and x = 10, you get
(a) $10 million (wouldn't that be nice)
(b) $100
(c) $2000
(d) $12,100 (notice that this would be the value of the entire investment after using compound interest, but it's nowhere close to the interest alone)
(e) $22,000
the only one that's even remotely close to your compound-interest estimate is (c), so you should still get the problem correct.
although you get lucky this time; it's extremely common for at least one incorrect answer in a simple-interest problem to come from a compound-interest formula (or vice versa).

[kouranjelika]

Hi Ron,

Quick question on this, what if we were looking to calculate the entire investment's value with the simple interest rate after the time period. Would the formula look like this:

Pt(1+r/100)? I am plugging numbers and it won't work. I keep getting a larger number then I should, but I can't seem to understand how to modify the formula.

Also, why can't we use the compound formula for simply interest? Doesn't that simply (hehe simple-y :)) mean that we compound once (annually?). Or does simple interest rate almost assume we are taking this money out every year or something like this? Therefore only the original amount gets interest-ed?

So how would you do the formula then? Just P + Pt(r/100)?

Perhaps I just hit it, but am I correct?

Thank you!

[RonPurewal]

Hi Ron,

Quick question on this, what if we were looking to calculate the entire investment's value with the simple interest rate after the time period. Would the formula look like this:

Pt(1+r/100)? I am plugging numbers and it won't work. I keep getting a larger number then I should, but I can't seem to understand how to modify the formula.

Yeah, that won't work, because you're multiplying the entire value by "t".
The passing of time only affects the interest amount, not the principal (=original) amount.

You can derive the expression:
Original amount + (Original)(% per year)(Number of years)
P + Prt
or, P(1 + rt)

This is with r expressed as a decimal, not a whole number. E.g., if the interest rate is 6%, then that's r = 0.06, so that the formula is P + 0.06Pt.
If r represents the whole number (r = 6 instead of r = 0.06), then the formula would be P + (Prt/100), or P(1 + (rt/100)).

[RonPurewal]

Also, why can't we use the compound formula for simply interest?

They're fundamentally different concepts.

Compound interest"”regardless of how often (or how seldom) the interest is actually compounded"”is based on the latest value of an amount. It's based on all the money that is in the bank, including the interest accrued from previous compounding steps.

Simple interest is calculated as a percentage of the original or starting amount. When interest is accrued, it is not taken into account.

Simple interest thus adds exactly the same amount of interest every period, while compound interest amounts will increase as time goes on (since they are based on increasing amounts of money in the bank).

[RonPurewal]

Yeah, simple interest is a bit weird. But it's a LOT easier to calculate than compound interest. For instance, if a legal settlement is $10,000 and accrues 10% simple interest for each year it is outstanding, then that's just another $1000 in interest each year.
With compound interest compounded annually, there's $1000 in interest the first time, but then $1100 the second time, $12100 the third time, and so on. The numbers get weird pretty quickly"”even more quickly if compounding is more frequent.

Because simple interest is easy, it's used in many situations involving calculation of interest by non-finance professionals. For instance, civil court judgments accrue 10% simple interest in most states, because it's for the best if court employees (who are not finance specialists) don't have to be encumbered with compound interest calculations.
Bankers use compound interest because that's what banking is all about.

[RonPurewal]

Or does simple interest rate almost assume we are taking this money out every year or something like this?

This is a useful analogy for how simple interest works"”although simple interest works this way without withdrawals/payments/reductions of the principal amount.

[kouranjelika]

Hi Ron,

Sorry responding so late. Thank you so much for this and all the other answers. I'm totally under water and didn't mean to be rude.

Thanks again!

[RonPurewal]

Hi Ron,

Sorry responding so late. Thank you so much for this and all the other answers. I'm totally under water and didn't mean to be rude.

Thanks again!

No worries.

If you're underwater, try to come up for breath every now and then.
(: