Loan Repayments

Jack and Jill take out an investment loan to purchase a rental property
worth $980,000.  They have a deposit of $100,000.  The loan is to be repaid in equal monthly instalments over a term of 10 years

SOLUTION
You have purchased a rental property worth $980,000 by using an investment loan with the interest of 7.29% pa nominal with interest added monthly. Then, you will repay in equal monthly instalments over a term of 10 years. Your first deposit is $100,000.  Therefore, this report will address problems regarding of your investment loan for the rental property.

a) Monthly repayments
The monthly repayments are $10,349.56
Supporting calculation:
Amount borrowed is 980,000 – 100,000 = 880,000 Interest rate is 7.29% per year, which implies .0729/12 or .6075% or .006075 per month The term is 10 years, which gives 10 x 12 or 120 repayments. Repayments = 880,000/PVIFA(120, .006075)  = 10,349.56

b) Interest claimed for tax purpose

By getting the total interest of each 12 months period, we have the interest in very year over 10 years. And the interest you need to claim each year for tax purpose is shown in the figure 1. The chart has demonstrated that the interest decreases years after years. It can be explained that the principle payments are reduced after one payment has been made each year.

c) If you decide to pay out the loan immediately before making the 50th payment, you will need to pay the amount of $599,043.02. It has been calculated as below.

Balance owing after the 50th payments: 

PV = C x PVIFA(r,n)

= 10,349.56×[1 – (1 + .006075)^(-70) ]/.006075

= 588,693.47

Balance owing just before the 50th payment: 

PV             =           588,693.47 + 10,349.56

               =          599,043.02

d)At the end of year three of the loan, a gift of $100,000 is put against the loan to do either option 1 or 2:
  1.Keep the same term and reduce monthly payments
  2.Keep the same monthly payments and reduce the term

Data analysis:

Principle payment after year 3:         679,334.86 

After year 3, there are still 84 payments to go.

Principle payments after put 100,000 against the debts: 679,334.86 - 100,000 = 579,334.86

For option 1: The new repayment will be: $8,826.07 by using the formula PV = C x PVIFA(n,r)

Supporting calculation: 

PV   =  C x PVIFA(n,r)

        =  C x {[1-(1+r)-n]/r}

Therefore:  C      =  PV/PVIFA(n,r)

                              =  PV/{[1-(1+r)-n]/r}

        =  579,334.86/{[1-(1+ .006075)-84]}/ .006075

        =  8,826.07

For option 2: According to the repayment schedule (table 2), after adding $100,000 to the payments, 15 months are reduced. There are only 105 payments remaining, and you only have to pay $6,422.96 instead of $10,349.56 in the last payment (105th payment).

As it is shown in figure 2, if you choose option 1, your monthly repayment will be $8,826.07. In other words, you will save the amount of $1,523.48 per month over 84 months remaining. However, if you prefer option 2, you will finish off the loan term quicker than option 1 by 15 months, thus no interest charged for 15 months. Two options have their own benefits; hence the best option would depend on debtors’ budgets for the months.