Final answer:
To determine the loan option with the lowest overall cost and the potential savings over other options, one must compare the total cost of the subsidized, unsubsidized, and private loans, taking into account their respective interest rates and terms. The subsidized loan will not accumulate interest during school, while the unsubsidized and private loans will. However, the unsubsidized loan has a lower interest rate than the subsidized loan, and the private loan has the longest term.
Step-by-step explanation:
To compare the total costs of the different student loan options, we need to take into account the interest rates and terms of each loan type. Since payments are deferred for 6 months and interest is capitalized, this will also affect the total amount paid over the life of the loan.
Subsidized Loan Calculation
For a subsidized loan with a 7.5% interest rate over 10 years, no interest is accumulated while in school because the government covers the interest during this period. The interest will start accumulating after the 6-month grace period post-graduation.
The total cost of the subsidized loan can be computed using the formula for the future value of an ordinary annuity because the loan payments are made at the end of each period (i.e., year). This calculation would require finding the monthly payment first and then multiplying by the number of months to get the total amount paid over 10 years. The calculation can be complex and usually requires financial calculator or software.
Without the exact monthly payment calculation here, we cannot give an absolute value. However, to find which loan has the lowest overall cost, we need to compare this subsidized loan with the other options based on the given interest rates and terms.
The total cost of each loan option would typically be calculated using an amortization formula or a financial calculator. Each payment would consist of a portion of the principal and a portion of the interest. The payments would sum to the total cost over the life of the loan.
Calculating Savings
The amount saved by choosing one option over the other would be the difference between the total cost of the least expensive loan and each of the other loan options. This can be determined once the total cost for each loan is calculated.