The quarterly payment is $300 over 6 years. We assume that she is just graduating when the loan is taken out. Therefore payback will be 24 (6x4) pay periods for which she can afford to pay the $300. Whenever an interest rate is presented by a bank it is assumed to be an annual rate. Therefore a 7% rate needs to be converted to a quarterly compound interest rate of 7% / 4 or .07/4 = .0175. The general equation for calculating a periodic payment is:
Q = L × r(1 + r)n / ((1 + r)n -1)) where Q = quarterly payment and L = amount of loan, n =24, and r = .0175.
We need to find the amount of loan she can take out, given she will afford to pay $300 every quarter. Therefore we need to solve for L.
L = Q/( r(1 + r)n / ((1 + r)n - 1))) = Q × (1 + r)n -1) / r(1 + r)n = 300 × (1 + .0175)24 -1) / (.0175*(1 + .0175)24)
L = $5838.21
