Final answer:
The question involves calculations of maximum loan amounts and payment schedules based on financial terms such as interest rate and amortization period. Using these values, the use of formulas such as the present value of an annuity can help determine the amount that can be borrowed and the total repayment amount over the life of the loan.
Step-by-step explanation:
The student's question pertains to the calculation of loan amounts and payments based on various financial constraints and terms provided by a bank. This involves understanding concepts related to loans such as interest rates, amortization, payment frequency, debt service coverage ratio, and loan to cost ratios. To answer the student's question accurately, one must apply mathematical formulas that determine loan payments and maximum loan amounts allowable under specific financial conditions.
Example Calculations
For instance, if Joanna can afford to pay $12,000 a year for a house loan, with interest rates at 4.2% annually and amortization over 30 years, we can use the present value formula to find out the maximum loan she can afford:
Using the present value of an annuity formula:
PV = PMT × (1 - (1 + i)^{-n}) / i
Where PV is the present value (the maximum loan amount Joanna can afford), PMT is the annual payment ($12,000), i is the annual interest rate (4.2% or 0.042), and n is the total number of payments (30 years).
Adjusting for the fact the payments are annual, the calculation simplifies to present value of an ordinary annuity formula, since payments and interest rates coincide on an annual basis.
After making the appropriate calculations, Joanna would be able to find out the maximum loan value she can afford and the total amount she would end up paying over 30 years.