Mimi bought a piece of land for RM100,000. She made an initial down payment of 20% from the cash price and the balance is financed through a bank for 5 years.
i. If the bank's rate is 12% compounded monthly, find the monthly payments that Mimi made to settle the loan.
ii. If Mimi intends to settle the loan by making a final payment immediately after paying the first 40 monthly payments, find the value of this payment.
iii. Suppose Mimi missed the first five payment. How much should be paid on the sixth month if she wanted to settle the outstanding arrears?
i.
First, calculate the amount financed by the bank:
Amount financed = RM100,000 - 20% of RM100,000 = RM100,000 - RM20,000 = RM80,000
Next, use the formula for calculating monthly payments for a loan:
PMT = [P*r(1+r)^n] / [(1+r)^n - 1]
Where:
PMT = Monthly payment
P = Principal amount (RM80,000)
r = Monthly interest rate (12% annual rate divided by 12 months = 1% or 0.01)
n = Number of months (5 years x 12 months = 60 months)
PMT = [RM80,000*0.01*(1+0.01)^60] / [(1+0.01)^60 - 1]
PMT = [RM80,000*0.01*(1.01)^60] / [(1.01)^60 - 1]
PMT = [RM80,000*0.01*(1.822)] / [(2.226) - 1]
PMT = RM1,456.75
Therefore, Mimi's monthly payments to settle the loan will be RM1,456.75.
ii.
After making the first 40 monthly payments, there will be 20 remaining payments. To find the final payment value, use the formula:
Balance = PMT * [(1- (1 + r)^-n) / r]
where n = 20 months
Balance = RM1,456.75 * [(1- (1+0.01)^-20) / 0.01]
Balance = RM1,456.75 * [(1- (1.2214) / 0.01]
Balance = RM1,456.75 * [(0.2214) / 0.01]
Balance = RM3,228.06
Therefore, Mimi's final payment after paying the first 40 monthly payments will be RM3,228.06.
iii.
If Mimi missed the first five payments, she would have an outstanding arrears of:
Arrears = 5 * RM1,456.75 = RM7,283.75
Therefore, Mimi should pay RM7,283.75 on the sixth month to settle the outstanding arrears.