 # Interest Anually, Compounded Continuosly

I decide that a year from now I`m going to invest in \$100 in an investment account that pays 8% interest anually, compounded continuosly. What will the investment be worth in 12 years?

I tried LN(1,08) = 0,076961041

i = 7,696104114

PV = 100 CHS

N = 12

0 PMT

FV = 243,4444

Why is it wrong???

When you use the TVM buttons on your calculator, what sort of interest rate do you need to use? Continuous? Effective? Nominal?

I believe it should be 100e(0.08x12) = 261.17

Look at the example in the TVM chapter, for continuous compounding.

In addition to Analyst0718, you can work backwards to 8% annual interest rate by:

-> ln(261.17/100) = 0.96

-> 0.96 divided by 12 = 0.08 or 8%

But thats `s because you need to use N = 11 I guess

Continuous, But I don`t know a way of doing it using the TVM buttons, maybe only applying the formula…

that part is easy to miss if you try and rush the problem. you are investing 100 a year from now (that is, at t = 1) an not right-away. 12 years from now, 11 years will have passed since you invested 100 dollars, which means N should be 11 as you pointed out.

You’re right, because it says “A year from now”.

Not continuous.

Next guess?

How it`s not?

pays 8% interest anually, compounded continuosly.

If it`s not continuous it`s probably nominal than, but that doesn`t make sense…

Guess again.

You got that part right.

the magician is asking what value would you have to enter in I/Y so that, after entering N and PV you can find the future value using FV. it is worth noting that there is no dedicated button for continuous compound rate, though you could use iconv, set 8% as the nominal rate and an arbitrarily high value for the C/Y (99999 should be good enough), then asking the calculator for the effective rate. the EFF rate given by iconv is slightly below the true effective rate, but should be very close, and certainly close enough to the true effective rate for solving the problem.

having said that, i see no real reason to use the TVM functionality for this problem when it is cumbersome (you have to use iconv to even get the interest rate you need) and prone to error (if your P/Y was set to a number other than 1 as a result of solving another problem and forgot to change it back to 1, you would get a wrong answer as a result, even if your other inputs were correct)

So, Effective?

I decide that a year from now I`m going to invest \$100 in an investment account that pays 8% interest anually, compounded continuosly. What will the investment be worth in 12 years?

I figured out a way to do this in HP12c thorugh is a little tricky:

8 enter 1 million divide - i

11*1 million - N

PV = CHS 100

0 PMT

FV I get the right answer: 241,0899622

Too bad I`m not a BA II Plus user to do that Try 525,600.  Yes.

I’m getting the impression that you may not have a solid understanding of what an effective interest rate is. Or a nominal interest rate. Or a continuously compounded interest rate.

You would benefit from such understandings, I believe.

In any case, you’re given an 8% (nominal) rate, compounded continuously. You need an effective rate. How do you get from a (nominal) continuously compounded rate to an effective rate?

Better still in knowing how to do it properly. The formula’s in the curriculum, and the approved calculators each have a button for it.

I did 525.600 in a exercise before, but it wasn`t as consistent as doing 1M…  