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. To find the monthly payments, we need to first calculate the loan amount financed by the bank. Since Mimi made an initial down payment of 20% of the cash price, the loan amount is 80% of the cash price.
Loan amount = 0.8 * RM100,000 = RM80,000
Next, we need to calculate the monthly interest rate. Since the bank's annual rate is 12% compounded monthly, the monthly interest rate is 12%/12 = 1% or 0.01.
To calculate the monthly payments, we can use the formula for the monthly payment on a loan:
Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Number of months))
Number of months = 5 years * 12 months/year = 60 months
Monthly payment = (RM80,000 * 0.01) / (1 - (1 + 0.01)^(-60))
= RM1600 / (1 - (1.01)^(-60))
≈ RM1600 / (1 - 0.3769)
≈ RM1600 / 0.6231
≈ RM2,570.60
Therefore, Mimi made monthly payments of approximately RM2,570.60 to settle the loan.
ii. Mimi intends to settle the loan by making a final payment immediately after paying the first 40 monthly payments. This means she will make 40 monthly payments of RM2,570.60.
To find the value of the final payment, we can calculate the remaining loan amount after 40 payments and add the interest for the remaining period.
Remaining loan amount after 40 payments = Monthly payment * (1 - (1 + Monthly interest rate)^(-Number of payments))/ Monthly interest rate
= RM2,570.60 * (1 - (1 + 0.01)^(-40))/ 0.01
≈ RM2,570.60 * (1 - 0.3305) / 0.01
≈ RM2,570.60 * 0.6695 / 0.01
≈ RM1,720.44
To find the value of the final payment, we need to add the interest for the remaining period. Since the remaining period is 20 months, the final payment can be calculated as:
Final payment = Remaining loan amount + (Remaining loan amount * Monthly interest rate * Number of remaining months)
= RM1,720.44 + (RM1,720.44 * 0.01 * 20)
= RM1,720.44 + (RM344.09)
≈ RM2,064.53
Therefore, the value of the final payment is approximately RM2,064.53.
iii. If Mimi missed the first five payments, the outstanding arrears would be the total of the missed payments.
Outstanding arrears = 5 payments * RM2,570.60
≈ RM12,853
Therefore, if Mimi wanted to settle the outstanding arrears on the sixth month, she should pay approximately RM12,853.