Question

Case Study for Financial Management.

Case 1
You want to buy a house that costs $140,000. You have $14,000 for a down payment, but your credit is such that mort- gage companies will not lend you the required $126,000. However, the realtor persuades the seller to take a $126,000 mortgage (called a seller take-back mortgage) at a rate of 5%, provided the loan is paid off in full in 3 years. You expect to inherit $140,000 in 3 years, but right now all you have is $14,000, and you can afford to make payments of no more than $22,000 per year given your salary. (The loan would call for monthly payments, but assume end-of-year annual payments to simplify things.)

a. If the loan was amortized over 3 years, how large would each annual payment be?  
Could you afford those payments?
b. If the loan was amortized over 30 years, what would each payment be? Could you afford those payments?
c. To satisfy the seller, the 30-year mortgage loan would be written as a balloon note, which means that at the end of the third year, you would have to make the regular payment plus the remaining balance on the loan. What would the loan balance be at the end of Year 3, and what would the balloon payment be?

Case 2

Six years from today you need $10,000. You plan to deposit $1,500 annually, with the first payment to be made a year from today, in an account that pays a 5% effective annual rate. Your last deposit, which will occur at the end of Year 6, will be for less than $1,500 if less is needed to reach $10,000. How large will your last payment be?

Answer 1

A )

Rate of Interest	5% p.a
Loan Amount	$126,000
Tenure of Repayment	3 Years

Annual Equated Payment = (P X R X (1+R)^N) / (((1+R)^N)-1)

Where:

P : Principle

R : Rate of Interest Per annum N : Period of Repayment

Annual Equated Payment = (126000 x 5% x (1 + 0.05) ^ 3 ) / ((1 + 0.05) ^ 3) - 1

                                                     = (6300 x (1.05^3)) / ((1.05^3) – 1

                                                     =7293.04 / 0.1576

                                                    = $ 46,268.28 per annum

Since from Salary income maximum amount that can afford is $ 22,000 per annum and above Annual Equated payment is $ 46,268.28 per annum and hence above amount can’t be paid back in period of 3 years

B)

Rate of Interest	5% p.a
Loan Amount	$126,000
Tenure of Repayment	30 Years

Annual Equated Payment = (P X R X (1+R)^N) / (((1+R)^N)-1)

Where:

P : Principle

R : Rate of Interest Per annum N: Period of Repayment

Annual Equated Payment = (126000 x 5% x (1 + 0.05) ^ 30 ) / ((1 + 0.05) ^ 3) - 1

                                                   = (6300 x (1.05 ^ 30)) / (1.05 ^ 30) – 1

                                                   = 27,228.24 / 3.32

                                                   = 8196.48 per annum

If repayment period is 30 years you can afford to pay above annual equated payment of $ 8196 per annum from your salary income of $ 22,000 per annum.