Question

Project Details

John and Jane Doe are newlyweds with executive track careers at ACME Gadget Company. In five years, the Does would like to have a family, envisioning two young children, Jack and Jill. With an eye for the future, John and Jane are now looking to ensure that their future family has a place to call home, that their future children will have access to all the education they desire, and that they themselves will be able to enjoy retirement when the time comes. As such, they’ve come to your financial planning company for advice for purchasing a house, planning for retirement, setting up a RESP and for your perspective on a side venture. They’ve provided you with the background and questions below.

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?

Please include diagram and complete on Microsoft word thank you.

Answer 1

According to the original plan, the PV of the contribution every month for the next 5 years will be-

FV = 60000 I / 4 = 2.5 / 12 N = 5 * 12 PMT = 1000

So, we get PV = 109303

But after lending the money of 65000 repaying it at the original plan will not be fair as they will not be getting the money they deserve according to the interest.

So, using a financial calculator, we will calculate the monthly payment.

PV = -65000 N = 5 * 12 I / Y = 2.5 / 12 FV = 0

Then, we get PMT = 1154

So, to be fair their monthly installment increases by 154 every month

___________________________________

For the first case,

Interest rate from an AP series starting from Year 1 to Year 25

25, 2.75, …. 8.5

Sum of an AP series = 25 / 2 * (2.5 + 8.5)

= 275 / 2

Therefore, we take the average at the interest rates

275 / (2 * 25) = 5.5%

So, using a financial calculator

PV = -500000N = 25 * 12 I / 4 = 5.5 / 12 FV = 0

So, we get PMT = 3070.4

For the second case,

Interest rate from an AP series starting from Year 1 to Year 25

3.5, 3.75, …. 9.5

Sum of an AP series = 25 / 2 * (3.5 + 9.5) = 325 / 2

Therefore, we take the average of the interest rate 325 / (2 * 25) = 6.5%

So, using a financial calculator

PV = -500000N = 25 * 26 I / 4 = 6.5 / 26 FV = 0

So, we get PMT = 1557

So, they should accept the first mortgage plan.