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.
i. First, we need to calculate the balance that Mimi financed through the bank.
Down payment = 20% of RM100,000 = 0.20 x RM100,000 = RM20,000
Balance financed = RM100,000 - RM20,000 = RM80,000
Using the formula for monthly loan payment:
M = P [ r(1 + r)^n ] / [ (1 + r)^n - 1 ]
Where:
M = monthly payment
P = principal amount (loan amount) = RM80,000
r = monthly interest rate = 12% / 12 = 1% = 0.01
n = number of monthly payments = 5 years x 12 months/year = 60 months
M = RM80,000 [ 0.01(1 + 0.01)^60 ] / [ (1 + 0.01)^60 - 1 ]
M = RM80,000 [ 0.01(1.01)^60 ] / [ (1.01)^60 - 1 ]
M = RM80,000 [ 0.01(1.822) ] / [ 1.822 - 1 ]
M = RM80,000 [ 0.01822 ] / 0.822
M = RM1,776.40
Therefore, Mimi made monthly payments of RM1,776.40 to settle the loan.
ii. To find the value of the final payment after 40 monthly payments, we need to calculate the remaining balance after 40 payments.
Remaining balance after 40 payments:
Using the formula for remaining balance in a loan after n monthly payments:
B = P [(1 + r)^n - (1 + r)^p] / [(1 + r)^n - 1]
Where:
B = remaining balance
P = principal amount (loan amount) = RM80,000
r = monthly interest rate = 0.01
n = total number of monthly payments = 60
p = number of payments made = 40
B = RM80,000[(1 + 0.01)^60 - (1 + 0.01)^40] / [(1 + 0.01)^60 - 1]
B = RM80,000[(1.822 - 1.488) / 0.822
B = RM80,000[0.334 / 0.822]
B = RM32,524.39
Therefore, Mimi's final payment after 40 monthly payments would be RM32,524.39.