Final answer:
To advise Keith on whether he should consolidate his loans, one must calculate and compare the total interest paid over the life of his current and potential consolidated loans using the formula for loan payments and factoring in the various interest rates and loan terms.
Step-by-step explanation:
To determine if Keith should take the consolidation option for his student loans, we need to compare the total interest he would pay for the existing loans and the proposed consolidated loan.
For the $19,000 loan at an APR of 6% for 12 years:
Using the formula for loan payments, the monthly payment P can be calculated as P = rPv/(1 - (1 + r)^-nt), where Pv is the present value of the loan, r is the monthly interest rate, n is the number of monthly payments, and t is the number of years. Calculating with this formula, we find Keith's monthly payment. Multiplying this by 12 to get the yearly payment and then by 12, the number of years, gives us the total amount paid. Subtracting the principal from this gives us the total interest paid on the first loan.
For the $25,000 loan at 7% for 8 years, we perform a similar calculation to find the monthly payment and then the total interest paid over the life of the loan.
Comparing these interests to the interest Keith would pay with the consolidated loan of $44,000 at 6.5% for 10 years, we apply the same loan formula to find the monthly and total payments, and from there, the total interest paid.
The option with the lower total interest cost is the better financial choice for Keith. Factors such as his ability to make regular payments and stability of income should also be considered, as they can affect the feasibility of maintaining the chosen repayment strategy.