Final answer:
To determine the total sum of all monthly payments, the loan amount is multiplied by a factor derived from the APR and the total number of payments. The monthly interest rate and the total number of payments over 30 years are used in the calculation. The final sum will include all monthly payments over the 30-year term.
Step-by-step explanation:
To calculate the total sum of all monthly payments for David and Kennah's 30-year loan of $258,449 at an annual percentage rate (APR) of 2.78%, you will need to use the formula for calculating the total payment of an installment loan: Loan Payment = Loan Amount x (interest rate / 12) / (1 - (1 + interest rate / 12)^(-n)), where 'n' is the total number of payments (months).
First, find the monthly interest rate by dividing the annual rate by 12: 2.78% / 12 = 0.2316% (monthly rate). To determine 'n', multiply the number of years (30) by 12 months: 30 x 12 = 360 months.
Substituting these values into the loan payment formula will give us the monthly payment, which can then be multiplied by 360 to find the total sum of all monthly payments required to pay off the loan. However, the final answer will be affected by rounding each monthly payment to the nearest whole number.