# Thread: Need help with annualized*yield*calculation

1. ## Need help with annualized*yield*calculation

Hello everyone, I've been stumped on finding a solution for the following problem and was hoping you could help me out.
I am trying to find the interest percentage for the following problem and the formula for solving it.

The goal is to find the interest rate needed to reach 1,035,479.

Code:
Beginning   Days    Deposits    Interest      Balance
240,000     0        0            0         240,000
240,000    365     41,514       69,647      351,161
351,161    365     41,514      101,905      494,580
494,580    365     41,514      143,525      679,619
679,619    365     41,514      197,834      918,967
918,967    171       0         116,512     1,035,479
Now, the answer to this problem is roughly 25.4882460120608%.
But I can't seem to find a formula to come to this answer.

Any help would be most appreciated.

2. Cannot be calculated by formula.
Iteration (fancy term for "hit and miss"!) required.

By the way, how did you get 25.488...% ?
69647 / 240000 = .29019.... hence real close to 29%.

3. ## More detail

Thanks Wilmer.

The interest is compounded daily and the following formula is used to calculate the amount of interest in the Interest column.

(APY) Interest amount = (((1 + (Interest Rate/365))^days)*balance)-balance

In the current problem it would look like (((1 + (25.488...%/365))^365)*240,000)-240,000 = 69,647

I'm trying to create a coded function that will do the calculation, so any details on the exact iteration process needed would help.

4. Well then, that sure makes the problem easier.
Since 69647 as the interest on 240000 for 365 days is a given,
then the effective annual rate = 69647 / 240000 = .2901958....

This rate is achieved by compounding daily, hence:
(1 + i)^365 = 1.2901958
1 + i = 1.2901958^(1/365)
i = 1.2901958^(1/365) - 1 = .0006983...
annual equivalent: .0006983 * 365 = ~.25488

Amen.

5. Sorry to be going in circles. I keep leaving out important details it seems.
The interest (69647) is not given in the problem I'm trying to solve.
The only known values are the starting value, the days between deposits, the deposit amount, and what they should come to (1,035,479).
The reason the interest is given in my example is because it has been already solved in that instance.

6. Originally Posted by CptHector
The only known values are the starting value, the days between deposits, the deposit amount, and what they should come to (1,035,479).
You need another information, WHEN the 1,035,479 is to be reached.
Like, is the 171 days of 5th year a given?

7. Here is the table again except with only the known values.

Code:
Beginning   Days    Deposits    Interest      Balance
240,000     0        0            0         240,000
365     41,514
365     41,514
365     41,514
365     41,514
171       0                    1,035,479

8. Ahhh...I see...wish you had started off with this!!

As I said before, ITERATION is required.
Have a look here (don't faint!):
www.math.mcgill.ca/~mei/Wei_Wu_Mei.pdf

I'm no expert on the process...so BYE.

9. Thanks for the link. It looks like I'll be learning Algebraic Iteration.