You Borrow money on a self liquidating installemnt loan (equal payments at the e
ID: 2484512 • Letter: Y
Question
You Borrow money on a self liquidating installemnt loan (equal payments at the end of each year, each payment is part principal part interest) Use the installment method - not straight line What is the annual payment? What is the total interest payments? After half the payments have been made, what percentage of the total interest has been paid (round to the nearest percentage point)? After half the payments have been made, what percentage of the total principal has been paid (round to the nearest percentage point)?Explanation / Answer
This is a case like mortgage loan where the following formula is applicable for determining the Euated Monthly Installments
M=[P*r*[(1+r)^n]]/[(1+r)^n1]. These variables represent the following inputs:
Using above formula
a) Monthly Payment = [801000*(0.012)*(1.012)^552] / [(1.012)^552 -1]
= 9625.3
Annual payment = 9625.3 * 12 = $115503
b) Total Interest Payment = total amount paid - total principal
= 115503 * 46 - 801000
=$4512138
c)
From D) principal cleared = 801000 - 771812 = 29188
amount paid in 23 years = 9625.3 * 12 *23 = 2656583
Interest component paid in 23 years = 2627395
% interest paid till 23 years = 2627395/4512138 * 100 = 58.23
d) Principal outstanding after 23 years
P = E * ((1+r)^n - 1) /(r * (1+r)^n) where n is number of payments outstanding in months, E - EMI, r is monthly rate of interest
= 9625.3 * ((1.012)^276-1))/(0.012*(1.012)^276) = 9625.3 * 25.904 / 0.3228
= $771812
% of total principal paid = 100* (801000 - 771812)/801000 = 3.64%
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