Question 1190651: what is the future value of an ordinary annuity having daily payments of 50 pesos for 30 days with an rate of 20% compounded daily? Found 2 solutions by CPhill, ikleyn:Answer by CPhill(1959) (Show Source):
You can put this solution on YOUR website! Here's how to calculate the future value of the ordinary annuity:
1. **Identify the given values:**
* PMT (payment amount per period) = 50 pesos
* n (number of periods) = 30 days
* r (interest rate per period) = 20% per year compounded daily. We need the *daily* interest rate: 0.20 / 365 ≈ 0.0005479 (approximately)
2. **Use the future value of an ordinary annuity formula:**
FV = PMT * [((1 + r)^n - 1) / r]
3. **Calculate:**
FV = 50 * [((1 + 0.0005479)^30 - 1) / 0.0005479]
FV = 50 * [(1.0165 - 1) / 0.0005479]
FV = 50 * [0.0165 / 0.0005479]
FV = 50 * 30.115
FV ≈ 1505.75 pesos
Therefore, the future value of the ordinary annuity is approximately **1505.75 pesos**.
I used the same general formula, but I did not round r = 0.2/365: I kept it as is.
So, my formula was
FV = 50 * [ ((1 + 0.2/365)^30 - 1) / (0.2/365) ].
It provides more precise calculations and makes final rounding only at the very end.
In such calculations, making rounding at the very end only
and do not making intermediate rounding is critically important
for precision and is STRONGLY RECOMMENDED.
Intermediate rounding like 0.20 / 365 ≈ 0.0005479, as the other tutor makes,
is traditionally considered as a non-appropriate way.
Also, I used MS Excel as my calculator. It works with 15-bit numbers.
My answer is 1511.99 pesos.
