Rainer Wandrew borrowed P 50,000.00 from Social Security System, in the form of calamity loan, with interest at 8% compounded quarterly payable in equal quarterly installments for 10 years. Find the quarterly payments.
To find the quarterly payments, we can use the formula for the equal payment series:
P = (R*(1-(1+r)^(-n))/r)
where:
P = loan amount borrowed = P 50,000.00
R = quarterly payment
r = interest rate per quarter = 8% = 0.08
n = number of quarters = 10 years * 4 quarters per year = 40
Plugging these values into the formula:
50,000 = (R*(1-(1+0.08)^(-40))/0.08)
Simplifying the formula further:
50,000 = (R*(1-(1.08)^(-40))/0.08)
50,000 = (R*(1-0.12213103)/0.08)
50,000 = (R*(0.87786897)/0.08)
50,000 = (10.98711213*R)
To solve for R, divide both sides of the equation by 10.98711213:
R = 50,000 / 10.98711213
R ≈ P 4,550.68
Therefore, the quarterly payments are approximately P 4,550.68.