Question

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1. You find a home that you can purchase for $295,000. You make a 20 percent down-payment on the home. You find a savings bank that will write a loan for 30 years at a 4.5 percent annual rate with monthly payments that include interest and principal. Calculate the monthly payment.

2. Assume you are to receive a 25-year annuity with annual payments of $100. The first payment will be received at the end of Year 1, and the last payment will be received at the end of year 25. You will invest each payment in an account that pays 5.5 percent. What will be the value in your account at the end of Year 25? End of Year 30?

Answer 1

1.) Price of the Home is $ 295000, down payment is 20% of $295000 = 59000, Loan Amount = $295000- $59000 = $236000. Monthly payment = Loan Amount / Present value Annuity factor @ 0.375% for 360 period (4.5% /12 for 30 x 12)

PV annuity factor = ((1+ X)^(n)-1)/ X x ((1+X)^n)

Here X= 0.375% = .00375, n = 360, (1.00375^360) - 1 / 0.00375 x (1.00375^360) = 197.361

Monthly repayment = $236000/197.361 = $1195.78 per month

2.) The value of $100 PA invests for 25 years @5.5% PAin your account at the end of Year 25, here the future vallue annuity factor is to be used. the future value annuity factor for 25 years @5.5% PA. Future value annuity factor = (1 + X)^n - 1 / X. Here X = 5.5% or 0.055, n = 25. FVAfactor = 1.055^25 - 1 / 0.055 = 51.1526,Total future value = Amount x Future value annuity factor = 100 x 51.1526 = $ 5115.26

End of 30 years = here X remained same only n will be changed and is 30,

then FV annuity factor = 1.055^30 - 1 / 0.55 = 72.4355, total amount will be 72.4355 x 100 = $7243.55

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