A recent graduate's student loans total $13,000. If these loans are at 4.1%, compounded quarterly, for 9 years, what are the quarterly payments
Use
R=quarterly payment
i=interest = 4.1%/4 = 0.041/4
n = 9*4 quarters = 36 quarters
P = principal, present value = $13,000
Then
P(1+i)^n = R((1+i)^n-1)/i
Solve for R, everything else is known.
I get $433.65 (quarterly payment)
To calculate the quarterly payments on the student loans, we can use the formula for the future value of an annuity. The formula is:
FV = Pmt * [(1 + r/n)^(n*t) - 1] / (r/n)
Where:
FV = Future Value of the loan (which is $13,000 in this case)
Pmt = Quarterly payment
r = Annual interest rate (4.1%)
n = Number of compounding periods per year (quarterly, so 4)
t = Number of years (9)
Let's plug in the values into the formula:
$13,000 = Pmt * [(1 + 0.041/4)^(4*9) - 1] / (0.041/4)
Now, let's simplify and solve for Pmt:
$13,000 = Pmt * [(1.01025)^(36) - 1] / (0.01025)
To find the quarterly payment, we can isolate Pmt:
Pmt = $13,000 * (0.01025) / [(1.01025)^(36) - 1]
Using a calculator, we find:
Pmt ≈ $181.85
Therefore, the quarterly payments on the student loans would be approximately $181.85.