Question

In: Finance

Tony wants of open his own business. He needs a mortgage of $400,000 to build a...

Tony wants of open his own business. He needs a mortgage of $400,000 to build a plant to get his business started. After doing some research, he has decided that the best rate is 4.5% with semi-annual compounding. The mortgage is amortized for 25 years, but the initial contract is for 10 years with constant total payments.

1) What is the semi-annual payment?

2) Make a semi-annual mortgage repayment scheme showing for each time period the principal, principal repayment, interest, and cashflow. Format this appropriately.

3) At the end of the contract, after 10 years, how much does Tony still owe on the mortgage?

4) What effective interest rate is equivalent to 4.5% with semi-annual compounding?

5) What is the payment: • If Tony wants to make monthly payments? • If Tony wants to make weekly payments? • If Tony want to make daily payments?

6) What is the total amount paid annually under each of the payment frequencies from part 5)?

7) Which frequency pays the highest amount annually? Which pays the lowest amount annually? Why is there a difference?

8) Now assume that the interest rate for the remaining 15 years is anticipated to be 6.75% with monthly compounding. What is the payment if Tony makes weekly deposits?

9) If Tony makes weekly deposits for the whole 25-year period, how much money has Tony paid in total?

Expert Solution

1)

Present Value of Annuity = PMT * [1-(1+r)^-n]/r

Where, n = 25*2 = 50

r = 4.5/2 = 0.0225

Present Value of annuity = $ 400,000

So,

400000 = PMT * [1-(1+0.0225)^-50]/0.0225

400000 = PMT * [1-0.32873]/0.0225

400000 = PMT * 0.671274/0.0225

PMT = 400000/29.8344

PMT = $ 13,407.34

2)

Repayment schedule (In detail)

3)

At the end of contract, after 10 years, Outstanding Principal payment = $ 290,206.46 (from the above schedule)

4)

Effective Interest rate = (1 + r/n)ⁿ - 1

Effective Interest rate = (1.0225)²-1

Effective Interest rate = 1.04551 - 1

Effective Interest rate = 4.551 % p.a.

jeff jeffy answered 2 years ago

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