Answer:
The amount of one-time payment should he make on his 40th birthday to pay off his pension plan is P32,880.77.
Step-by-step explanation:
Step 1: Calculation of present value on 3 months after his 60th birthday
The present value on 3 months after his 60th birthday can be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PV60 = Q * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
Where;
PV60 = present value on 3 months after his 60th birthday = ?
Q = quarterly claim = P10,000
r = quarterly interest rate = annual interest rate / 4 = 8% / 4 = 0.08 / 4 = 0.02
n = number of quarters = number of years * Number of quarters in a year = 5 * 4 = 20
Substitute the values into equation (1), we have:
PV60 = P10,000 * ((1 - (1 / (1 + 0.02))^20) / 0.02)
PV60 = P10,000 * 16.3514333445971
PV60 = P163,514.33
Step 2: Calculation of one-time payment on his 40th birthday
The one-time payment can be calculated using the formula the following formula:
PV = PV60 / (1 + r)^n ........................ (2)
Where;
PV = Present value or One-time payment = ?
PV60 = present value on 3 months after his 60th birthday = P163,514.33
r = quarterly interest rate = annual interest rate / 4 = 8% / 4 = 0.08 / 4 = 0.02
n = number of quarters from 40th to 3 months after his 60th birthday = (number of years * Number of quarters in a year) + One quarter = (20 * 4) + 1 = 81
Substitute the values into equation (2), we have:
PV = P163,514.33 / (1 + 0.02)^81 = P32,880.77
Therefore, the amount of one-time payment should he make on his 40th birthday to pay off his pension plan is P32,880.77.
