Question

Loan amortization ( 25 points) Suppose Robert obtained a home mortgage loan from Wells Fargo Bank on September 1,2018 . The loan information is as follows: Loan amount: $350,000 Interest rate (p.a.): 4.86% Loan term: 30 years (paid monthly) Start date: September 1,2018 First payment date: October 1, 2018.

(1) Construct the amortization schedule for this mortgage loan. Please make sure you show the monthly payment, the proportion of interest and principal paid, and the ending balance for each scheduled payment date.
(2) Without considering the time value of money, estimate the total interests that will be over 30 -year loan term.
(3) Sensitivity analysis: Examine the same 30 -year $350,000 mortgage loan. If the mortgage rate per year were 3.00%,3.50%,4.00%,4.50%,5.00%,5.50%,6.00%, 6.50%, and 7.00%, what would be
(i) the monthly mortgage payment and
(ii) the total interest payments? Please construct a data table to answer the question.
(4) Draw a chart to show Robert's monthly loan payment, monthly interest payment, monthly principal repayment ( 3 curves) in one chart. Briefly explain their relationship

Answer 1

A loan amortization schedule can be constructed for a $350,000 loan at 4.86% over 30 years, with monthly payments of $1,798.65 and total payments of $647,514.57. Sensitivity analysis would reveal different monthly payments and total interest for rates from 3.00% to 7.00%. Additionally, an amortization chart can illustrate the relationship between the declining interest and increasing principal portions of each payment.

Step-by-step explanation:

Constructing a loan amortization schedule generally involves calculating the monthly payment, the division of that payment into interest and principal components, and the ending balance after each payment. To calculate these, the loan amount, interest rate, and loan term are needed. Given a loan amount of $350,000 with an annual interest rate of 4.86% over 30 years, the monthly payment can be determined using an amortization formula or a financial calculator.

If the monthly payment was calculated to be $1,798.65, over the loan term of 30 years, without considering the time value of money, the total amount paid would be $647,514.57, with the total interest paid being this amount minus the original loan amount.

Sensitivity analysis can be performed by calculating the monthly payments and total interest payments for interest rates ranging from 3.00% to 7.00%. A data table should be created showing these rates against the corresponding monthly payments and total interest over 30 years. Finally, a chart can be drawn to show the relationships among the monthly loan payment, monthly interest payment, and monthly principal repayment. These elements generally show that as more principal is paid down over time, the interest portion of each payment decreases.