Question

Money borrowed today is to be paid in 21 equal payments at the end of 21 quarters. If the interest rate is 15% compounded quarterly, how much was initially borrowed (in peso) if the quarterly payment is P1,532?

Answer 1

Given,

Quarterly payments = A = 1,532

r = rate of interest = 0.15

m = Number of weeks in a year = 52

n = Number of periods = 21

Present Value = PV =?

Hence by the following formula,

PV = [A / (r/m)] [1 – {1 + r/m} ^ (-n)]

      = [1532 / (0.15/52)] [1 – {1 + 0.15/52} ^ (-21)]

      = [1532 / 0.002884] [1 – 1/1.002884^21]

      = 531,206.657 [1 – 1/1.062342]

      = 531,206.657 [0.062342/1.062342]

      = 531,206.657 × 0.058683

      = 31,172.80

Answer: P 31,172.80