Final answer:
To calculate the additional interest accrued on Stephanie's student loan during a two-year deferment, we use the compound interest formula A = P(1 + r/n)^(nt), resulting in approximately $5,270.07 of interest.
Step-by-step explanation:
To determine how much additional interest Stephanie's student loan will accrue during a two-year deferment period, we need to use the formula for compound interest. The formula to calculate the future value of a compound interest loan is A = P(1 + r/n)nt, where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested or borrowed for, in years.
In Stephanie's case, P is $42,750, r is 6% or 0.06, n is typically compounded annually for student loans (n = 1), and t is 2 years. Hence, the formula becomes A = $42,750(1 + 0.06/1)1*2.
First, we calculate the growth factor: 1 + 0.06/1 = 1.06. Then raise it to the power of 2 (for the two years): (1.06)2. Subsequently, we multiply the principal by this factor: $42,750 * (1.06)2 ≈ $42,750 * 1.1236 ≈ $48,020.07.
Therefore, after two years, the loan will have grown to approximately $48,020.07. The additional interest added during the deferment is simply the difference between this future value and the original loan amount: $48,020.07 - $42,750 = $5,270.07.
So the additional interest that will be added to the loan at the end of the two-year deferment is approximately $5,270.07.