Question 1179819
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**.