Answer:
Explanation:
To determine which is lower, we need to compare the cash price of P16,000 with the present value of the installment term for the sala set priced at P2,950 per month for 6 months at 12% compounded semi-annually.
To calculate the present value of the installment term, we need to use the formula for present value of an annuity:
PV = PMT * (1 - (1 + r)^(-n)) / r
Where:
- PV = Present Value
- PMT = Payment per period
- r = Interest rate per period
- n = Number of periods
In this case, the payment per period (PMT) is P2,950, the interest rate per period (r) is 12% compounded semi-annually, and the number of periods (n) is 6 months.
First, let's convert the interest rate to a decimal and divide it by 2 to account for semi-annual compounding:
r = 12% / 2 = 0.12 / 2 = 0.06
Now, let's calculate the present value of the installment term:
PV = 2950 * (1 - (1 + 0.06)^(-6)) / 0.06
Using a calculator, we can find that the present value of the installment term is approximately P16,051.47.
Comparing this with the cash price of P16,000, we can see that the present value of the installment term is higher. Therefore, the cash price of P16,000 is lower than the present value of the installment term.
In conclusion, if you have the option to pay in cash or through monthly installments, it would be more cost-effective to choose the cash price of P16,000 rather than the installment plan.