Math

Dave takes out a 24-year mortgage of 290000 dollars for his new house. Dave gets an interest rate of 14.4 percent compounded monthly. He agrees to make equal monthly payments, the first coming in one month. After making the 68th payment, Dave wants to buy a boat, so he wants to refinance his house to reduce his monthly payment by 500 dollars, and to get a better interest rate. In particular, he negotiates a new rate of 7.2 percent compounded monthly, and agrees to make equal monthly payments (each 500 dollars less than his original payments) for as long as necessary, followed by a single smaller payment. How large will Dave's final loan payment be?

I knew there was a similar question,but I still cannot understand how to calculate.

  1. 👍 1
  2. 👎 0
  3. 👁 785
  1. first contract:
    i = .144/12 = .012
    n = 24(12) =288
    PV = 290000
    paym = ?

    paym( 1 - 1.012^-288)/.012 = 290000
    = ...... -----> X

    After making the 68th payment,
    balance of loan = 29000(1.012)^68 - X( 1.012^6868 = - 1)/.012
    = ...... Y

    This becomes the PV of a new contract,
    with
    new paym = X - 500
    i = .072/12 = ..006
    n = 288-68 = 220

    We don't know how many payments , (periods), we need, let that be n

    (X-500( 1 - 1.006^-n)/.006 ) = Y

    more than likely, n will be a decimal.
    Do not round up, round down
    e.g. suppose n = 34.8
    you will have to make 34 full payments of (X-500) and a partial paiment at period 35

    Have fun

    1. 👍 1
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. MATH

    Dave takes out a 24-year mortgage of 210,000 dollars for his new house. Dave gets an interest rate of 13.2 present compounded monthly. He agreed to make equal monthly payment, the first coming in one month. After making the 68th

  2. literature

    Buck had been purposely placed between Dave and Sol-leks so that he might receive instruction. Apt scholar that he was, they were equally apt teachers, never allowing him to linger long in error, and enforcing their teaching with

  3. math

    Dave wants to make a stone walkway. The rectangular walkway is 4 feet wide and 4 feet long. Each 2 foot by 2 foot stone covers an area of 4 square feet. How many stones will Dave need to make his walkway?

  4. physics

    Columnist Dave Barry poked fun at the name "The Grand Cities" adopted by Grand Forks, North Dakota, and East Grand Forks, Minnesota. Residents of the prairie towns then named their next municipal building for him. At the Dave

  1. literature

    Buck had been purposely placed between Dave and Sol-leks so that he might receive instruction. Apt scholar that he was, they were equally apt teachers, never allowing him to linger long in error, and enforcing their teaching with

  2. math

    Scott and Jen are looking at a house listed for 189000 dollars. They will qualify for a 6% interest rate if they have a 20% down payment. How much will the monthly payments be on a 15-year mortgage.I just don't understand what to

  3. Physics

    Dave needs to get groceries from the store, which is a distance of 1.7 km east of his house. Dave rides his bike to the store at a constant speed of 6.6 m/s, and rides back to his house at the slower speed of 2m/s. A)How long in

  4. math

    Dave is going to leave academia and go into business building grain silos. A grain silo is a cylinder with a hemispherical top, used to store grain for farm animals. Here is a 3D view, a cross-section, and the top view. If Dave is

  1. math

    Pick a Card. Mike and dave play the following card game. Mike picks a card from the deck If he selects a heart Dave gives him $5, if not, he gives Dave $2. Determine Mikes's expectation. Determine Daves' expectation Can you help

  2. geometrY

    to estimate the height of a tree, Dave stands in the shadow of the tree so that his shadow and the tree's shadow end at the same point. Dave is 6 feet 4 inches tall and his shadow is 15 feet long. If he is standing 66 feet away

  3. accounting

    House mortgage You have just purchased a house and have obtained a 30-year, $200,000 mortgage with an interest rate of 10 percent. Required: a. what is your annual payment? b. Assuming you bought the house on Jan. 1st, what is the

  4. Pre Calculus

    The diameter of a ferris wheel is 250 feet and θ is the central angle formed as Dave travels around the wheel. Dave starts his ride at Point 0, makes 4 complete revolutions and stops at Point 1, 45 degrees from Point 0. If his

You can view more similar questions or ask a new question.