Answer:
Ordinary Annuity:
Cash Value:
The cash price of Ms. Ribaya's car is ₱ 953, 702. 20. To solve for this, we need to understand several concepts including down payment (d), interest, present value (P), regular payment (R), interest rate per period (j), and the number of payments (n).
Solutions:
Given: ₱ 200, 000 - down payment
₱ 16, 200 - regular payment
10.5 % - interest which is compounded monthly so we will have
.105/12 = .00875 which is the interest rate per period
5 years - time
60 - number of payments which is given by 12 months x 5 years
First, find the present value of the car using the formula: P = R 1 - (1 + j)⁻ⁿ
j
P = R 1 - (1 + j)⁻ⁿ
j
P = ₱ 16, 200 (1 - 1 + .00875)⁻⁶⁰
.00875
P = ₱ 6, 594.89425
.00875
P = ₱ 753, 702. 20
Therefore, the present value of the car is P = ₱ 753, 702. 20.
Next, find the cash value of the car.
Cash Value = Present Value + Down payment
Cash Value = ₱ 753, 702. 20 + ₱ 200, 000
Cash Value = ₱ 953, 702. 20
Therefore, the cash value of Ms. Ribaya's car is ₱ 953, 702. 20.
Keywords: cash value, down payment, compound interest
