Question

Purchase of a new home

John and Jane had planned to save $60 000 dollars over the next five years as a down payment on a house. Jane assured John that if they contributed $1000 each month to a savings account that pays an annual rate of interest of 2.5% compounded monthly that they would have enough money to put a down payment of $60 000 on their new house. Wanting their daughter to have a house, Jane’s parents (The Henrys) have offered to lend John and Jane $65 000, which they have suggested (perhaps naively) John and Jane pay back by contributing to a savings account in the Henrys’ name as per Jane’s original savings plan. John’s worried this is not fair to his in-laws. Is he correct? If so, devise a fair repayment plan that would see the Henrys repaid at a rate of 2.5% compounded monthly over the 5 years.

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

1. A 5 year fixed rate with monthly payments at an annual interest rate of prime+1%
2. A 10 year fixed rate with biweekly payments at an annual interest 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 they accept given that their goal is to pay as much principle as possible over the next 10 years?

Teacher's notes:

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

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

If you want to ensure the Henrys earn interest as per Jane’s original payment plan, then you’ll need to calculate the PMTs needed 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 would have to be to ensure the Does pay back the Henrys 65 000 dollars with interest as per Jane’s original plan.

Answer 1