Question
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.
Answers
GPT 3.5
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.
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.