Horatio has taken out a $12,450 unsubsidized Stafford loan to pay for his four-year undergraduate education. The loan has an int
erest rate of 7.3%, compounded monthly, and a duration of ten years. Horatio will allow interest capitalization. Making monthly payments, how much interest will Horatio have paid in total by the time the loan is paid in full? Round all dollar values to the nearest cent.
I'll just give you an answer based on my understanding. I'll use the formula for compounding interest.
A = P(1+r/n)^nt
A = future value of the loan including interest P = principal of the loan r = interest rate n = number of times the interest is compounded per year (monthly=12) t = number of years the money is loaned for
Given: P = 12,450 r = 7.3%, compounded monthly t = 10 years
A = 12,450 (1+0.073/12)^12*10 A = 12,450 (1.006)¹²⁰ A = 12,450 (2.05) A = 25,522.50
25,522.50 - 12,450 = 13,072.50 total interest paid.
In this case, the equation that models the value of an initial investment of P dollars in t years at an annual interest rate of r is given by A = Pert.
