Purchase of a new home

John and Jane had planned to save $60 000 dollars over the nextfive years as a down payment on a house. Jane assured John that ifthey contributed $1000 each month to a savings account that pays anannual rate of interest of 2.5% compounded monthly that they wouldhave enough money to put a down payment of $60 000 on their newhouse. Wanting their daughter to have a house, Jane’s parents (TheHenrys) have offered to lend John and Jane $65 000, which they havesuggested (perhaps naively) John and Jane pay back by contributingto a savings account in the Henrys’ name as per Jane’s originalsavings plan. John’s worried this is not fair to his in-laws. Is hecorrect? If so, devise a fair repayment plan that would see theHenrys repaid at a rate of 2.5% compounded monthly over the 5years.

The Does have qualified for a mortgage of $500,000 to beamortized over 25 years. Their mortgage broker has offered them thefollowing options:

1. A 5 year fixed rate with monthly payments at an annual interestrate of prime+1%
2. A 10 year fixed rate with biweekly payments at an annualinterest rate of prime+2%

Prime is currently at 1.5% and projected to increase by 0.25%every year for the next 10 years. Which Mortgage terms should theyaccept given that their goal is to pay as much principle aspossible over the next 10 years?

Teacher's notes:

To begin you know the payment size, the number of payments andthe interest rated and what you need to determine is the FV ofthose payments using the formula: FV=PMT[((1+i)^n -1)/i].  

This will tell you how much money the Does will save (or payback to the Henrys) under Janes original plan. You can use thissame formula to ask how big the PMTs would have to be to ensure theDoes pay back the Henrys exactly 65 000 dollars. Of course thismeans the Henrys earn no interest.

If you want to ensure the Henrys earn interest as per Jane’soriginal payment plan, then you’ll need to calculate the PMTsneeded based on a present value of 65000 using the formula:PV=PMT((1-(1+i)^-n)/i). This will tell you how big the PMTs wouldhave to be to ensure the Does pay back the Henrys 65 000 dollarswith interest as per Jane’s original plan.