You Borrow money on a self liquidating installemnt loan (equal payments at the e
ID: 2488724 • 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) Loan $445,000 Interest Rate 11.40% Life (years) 50 Date of Loan January 1, 2016 Use the installment method - not straight line a) What is the annual payment? b) What is the total interest payments? c) After half the payments have been made, what percentage of the total interest has been paid (round to the nearest percentage point)? d) After half the payments have been made, what percentage of the total principal has been paid (round to the nearest percentage point)? You Borrow money on a self liquidating installemnt loan (equal payments at the end of each year, each payment is part principal part interest) Loan $445,000 Interest Rate 11.40% Life (years) 50 Date of Loan January 1, 2016 Use the installment method - not straight line a) What is the annual payment? b) What is the total interest payments? c) After half the payments have been made, what percentage of the total interest has been paid (round to the nearest percentage point)? d) After half the payments have been made, what percentage of the total principal has been paid (round to the nearest percentage point)?Explanation / Answer
a) Using the PMT function fo excel,
Annual payment = PMT(11.4%,50,-445000) = $50960
Using formula:
M = P(1+r)n r / [(1+r)n-1]
where M = yearly payment, r = rate of interest per period of payment and n number of payments, P = loan amount
M = 445000*((((1+11.4%)^50)*11.4%) /(((1+11.4%)^50)-1)) = $50960
b)
Total interest payment = total payment - borrowed amount = $50960 x 50 - $445000 = $2103000
c)
Half the payment is made at the end of 25 years.
Amortization Schedule for the first 25 years:
c)
Total Interest paid in the first 25 years = $1246025
% of total interest paid = $1246025 / $2103000 = 59.25%
d)
Total principal paid in the first 25 years = $27975
% of principal amount paid = $27975 / $445000 = 6.29%
year Instalment Interest Principal repayment Balance 0 $ 4,45,000 1 $ 50,960 $ 50,730 $ 230 $ 4,44,770 2 $ 50,960 $ 50,704 $ 256 $ 4,44,514 3 $ 50,960 $ 50,675 $ 285 $ 4,44,229 4 $ 50,960 $ 50,642 $ 318 $ 4,43,911 5 $ 50,960 $ 50,606 $ 354 $ 4,43,557 6 $ 50,960 $ 50,565 $ 395 $ 4,43,162 7 $ 50,960 $ 50,520 $ 440 $ 4,42,722 8 $ 50,960 $ 50,470 $ 490 $ 4,42,232 9 $ 50,960 $ 50,414 $ 546 $ 4,41,686 10 $ 50,960 $ 50,352 $ 608 $ 4,41,078 11 $ 50,960 $ 50,283 $ 677 $ 4,40,401 12 $ 50,960 $ 50,206 $ 754 $ 4,39,647 13 $ 50,960 $ 50,120 $ 840 $ 4,38,807 14 $ 50,960 $ 50,024 $ 936 $ 4,37,871 15 $ 50,960 $ 49,917 $ 1,043 $ 4,36,828 16 $ 50,960 $ 49,798 $ 1,162 $ 4,35,666 17 $ 50,960 $ 49,666 $ 1,294 $ 4,34,372 18 $ 50,960 $ 49,518 $ 1,442 $ 4,32,930 19 $ 50,960 $ 49,354 $ 1,606 $ 4,31,324 20 $ 50,960 $ 49,171 $ 1,789 $ 4,29,535 21 $ 50,960 $ 48,967 $ 1,993 $ 4,27,542 22 $ 50,960 $ 48,740 $ 2,220 $ 4,25,322 23 $ 50,960 $ 48,487 $ 2,473 $ 4,22,849 24 $ 50,960 $ 48,205 $ 2,755 $ 4,20,094 25 $ 50,960 $ 47,891 $ 3,069 $ 4,17,025 Total $ 12,74,000 $ 12,46,025 $ 27,975 $ 109,02,074Related Questions
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