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Question 1179819: f. Find the present values of the following annuities
i. RM6,000 every year for 8 years at 12% compounded annually
ii. RM800 every month for 2 years 5 months at 5% compounded monthly
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's calculate the present values of these annuities:
**i. RM6,000 every year for 8 years at 12% compounded annually**
* **Payment (PMT):** RM6,000
* **Number of periods (n):** 8 years
* **Interest rate per period (r):** 12% or 0.12
We will use the present value of an ordinary annuity formula:
PV = PMT * [1 - (1 + r)^(-n)] / r
PV = 6000 * [1 - (1 + 0.12)^(-8)] / 0.12
PV = 6000 * [1 - (1.12)^(-8)] / 0.12
PV = 6000 * [1 - 0.403883] / 0.12
PV = 6000 * [0.596117] / 0.12
PV = 6000 * 4.96764
PV ≈ RM29,805.84
**ii. RM800 every month for 2 years 5 months at 5% compounded monthly**
* **Payment (PMT):** RM800
* **Number of periods (n):** (2 years * 12 months) + 5 months = 24 + 5 = 29 months
* **Annual interest rate:** 5% or 0.05
* **Monthly interest rate (r):** 0.05 / 12 ≈ 0.00416667
We will use the present value of an ordinary annuity formula:
PV = PMT * [1 - (1 + r)^(-n)] / r
PV = 800 * [1 - (1 + 0.00416667)^(-29)] / 0.00416667
PV = 800 * [1 - (1.00416667)^(-29)] / 0.00416667
PV = 800 * [1 - 0.887649] / 0.00416667
PV = 800 * [0.112351] / 0.00416667
PV = 800 * 26.96424
PV ≈ RM21,571.39
**Answers:**
i. The present value of RM6,000 every year for 8 years at 12% compounded annually is approximately **RM29,805.84**.
ii. The present value of RM800 every month for 2 years 5 months at 5% compounded monthly is approximately **RM21,571.39**.
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
f. Find the present values of the following annuities
i. RM6,000 every year for 8 years at 12% compounded annually
ii. RM800 every month for 2 years 5 months at 5% compounded monthly
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I checked calculations by @CPhill.
For calculations, I used MS Excel in my computer. This software is commonly considered
as a standard tool, which provides the necessary precision for such calculations.
For (i), I got the same value, so this part is correct.
For (ii), I got different value of RM 21810.41.
In this case, I used formula
PV =  .
I did not perform intermediate rounding: it is PROXIBITED in such calculations
and makes big influence, leading to incorrect answer.
I copy/pasted this my formula into Excel spreadsheet as is and got the answer in the next instance.
The difference in our predictions is 21810.41 - 21571.39 = 239 RM.
Such a great discrepancy in Finance calculations is not allowable and is not acceptable.
Overviewing calculations by @CPhill in many other his posts, I concluded,
that he is irresponsible in his calculations and does not care about their precision.
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