The table shows the specifications of an adjustable rate mortgage (ARM). Assume no caps apply. Find a) the initial monthly payment; b) the monthly payment for the second adjustment; and c) the change in monthly payment at the first adjustment. *The principal balance at the time of the first rate adjustment What is the initial monthly payment? (Round to the nearest cent.) CITO Beginning Balance Term Initial index rate Margin Adjustment period Adjusted index rate *Adjusted balance $90,000 20 years 6.5% 2.5% 1 year 8.0% $88,314.60
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- An interest rate obtained by dividing the nominal rate per year by the number of compounding periods in that year isa. A nominal interest rateb. An effective interest ratec. An effective interest rate only if the compounding period is monthlyd. Either (b) or (c)Which one of the following statements about a fixed-rate mortgage (FRM) loan is correct? a. The monthly payment of the FRM loan changes over the life of the loan. b. Each monthly payment contains the interest payment component and principal repayment component. The size of each component remains unchanged over the life of the FRM loan. c. Each monthly payment contains the interest payment component and principal repayment component. As time goes by, the size of the interest component increases and the size of the principal component decreases, but the sum of the two components remain unchanged. d. Each monthly payment contains the interest payment component and principal repayment component. As time goes by, the size of the interest component decreases and size of the principal component increases, but the sum of the two components remain unchanged.(Note, this is how mortgage payments are calculated.) Payments on a loan are amortized when a fixed amount is paid at the end of each time period in order to pay off both the principle of the loan and the interest accumulated up to that point. At the end of each period, interest is charged on the amount still owing. Let P be the initial amount of the loan, and i > 0 be the interest rate charged (per period), R the size of the per period payment (paid at the end of each period), and Pt the amount that is still owed after t periods. So P0 = P(a) Find P1.(b) Find a first order linear recurrence for Pt.(c) Show that the solution to your recurrence relation isPt = (P-(R/i))(1+i)^t + (R/i)
- Which of the following refers to the ratio of the interest to the principal repayment on an annual unpaid loan? A. it increases as the loan gets older О в. it decreases as the loan gets older O c. it remains constant over the life of the loan O D. it changes according to the level of market interest rates during the life of the loanCompute the present values of the following annuities first assuming that payments are made on the last day of the period and then assuming payments are made on the first day of the period: (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16)) Present Value Present Value Interest Rate (Payment made on last day of period) (Payment made on first day of period) Payment Years (Annual) 748.09 8. 14 % 8,668.26 14 7 21,022.93 24 70,412.54 32Construct a differential equation for the changing mortgage balance. (Equation Must include r, A, P, and dA/dt)Relevant information: monthly mortgage payment (M) is composed of taxes and insurance (TI), and principle and interest (P). So, M=TI + P (TI goes into escrow account). Mortgage rate, r, is APR divided monthly (0.05/12). t is time in months, A(t) is the mortgage balance after t months of payments. the rate of change of A(t) is the difference between interest incurred and P (the portion of the monthly payment that does not go into Escrow account).
- For compounding more frequently than annual, the effective interest rate Select one: a. is higher than the nominal rate b. is lower than the nominal rate c. depends on the amount borrowed 18 d. equal to the nominal rateFor compounding more frequently than annual, the effective interest rate Select one: a. equal to the nominal rate b. depends on the amount borrowed c. is lower than the nominal rate d. is higher than the nominal rateFind the monthly payment needed to amortize principle and interest for the fixed rate mortgage. Use eithr the regular monthly payment formula or the given table.
- Identify the following interest rates as nominal or effective. Rate 1: 1.5% per quarter Rate 2: 1.5% per quarter, compounded monthly (a) Both are nominal rates (b) Rate 1 is nominal and rate 2 is effective (c) Rate 1 is effective and rate 2 is nominal (d) Both are effective (e) None of the above a b d eWhich of the following statements regarding the interest rates is correct? I As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or less than the nominal rate on the deposit (or loan). Il If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by multiplying the periodic rate by the number of periods per year. III If a loan or an investment uses annual compounding, its nominal rate is also its effective rate I and III only II and III only I and II only Il onlyThe true rate of interest charged for a loan is called the ________ percentage rate. The true rate of interest charged for a loan is called the ▼ variable defined annual actual regular real percentage rate.