Sylvia takes a loan for $50,000 at 5% interest. She decides to pay the loan over
ID: 2793741 • Letter: S
Question
Sylvia takes a loan for $50,000 at 5% interest. She decides to pay the loan over 10 years using annual payments at the end of each year. a) Find her annual cost if she amortizes the loan b) Find her annual cost if she uses a sinking fund earning 6%. c) Find the net amount of interest she pays for both of these options. d) She decides to set her annual cost based on the amortization cost. But she pays only the interest due to the bank and deposits the balance in her using a sinking fund earning 6%. At the end of the 10 years she uses the Sinking Fund to repay the loan. How much is the balance of the Sinking Fund after she repays the loan?Explanation / Answer
Enter Values Loan Amount $ 50,000.00 Annual Interest Rate 5.00 % Loan Period in Years 10 Number of Payments Per Year 10 Loan amortization table - (a) Annual equivalent payments = Loan amount/ annuity factor(5%,10) = 50000/7.7217 6475.228689 PmtNo. Beginning Balance Scheduled Payment Principal Annual interest cost Ending Balance Cumulative Interest (payments - Interest) (Beginning balance x 5%) (Beginning bal. - principal) 1 $ 50,000.00 $ 6,475.23 $ 3,975.23 $ 2,500.00 $ 46,024.77 $ 2,500.00 2 46,024.77 $ 6,475.23 $ 4,173.99 $ 2,301.24 $ 41,850.78 $ 4,801.24 3 41,850.78 $ 6,475.23 $ 4,382.69 $ 2,092.54 $ 37,468.09 $ 6,893.78 4 37,468.09 $ 6,475.23 $ 4,601.82 $ 1,873.40 $ 32,866.27 $ 8,767.18 5 32,866.27 $ 6,475.23 $ 4,831.92 $ 1,643.31 $ 28,034.35 $ 10,410.50 6 28,034.35 $ 6,475.23 $ 5,073.51 $ 1,401.72 $ 22,960.84 $ 11,812.21 7 22,960.84 $ 6,475.23 $ 5,327.19 $ 1,148.04 $ 17,633.65 $ 12,960.26 8 17,633.65 $ 6,475.23 $ 5,593.55 $ 881.68 $ 12,040.11 $ 13,841.94 9 12,040.11 $ 6,475.23 $ 5,873.22 $ 602.01 $ 6,166.89 $ 14,443.94 10 6,166.89 $ 6,475.23 $ 6,166.88 $ 308.34 $ 0.00 $ 14,752.29 $ 14,752.29 (b) Sinking fund Method - PmtNo. Beginning Balance Scheduled Payment Sinking fund Investments Annual interest cost Ending Balance Sinking fund Closing balance Cumulative interest on sinking fund (payments - Interest) (Beginning balance x 5%) (Beginning bal. - principal) [(Lat yr balance x 1.06) + Current year payment] [Beginning balance x 6%) 1 $ 50,000.00 $ 6,475.23 $ 3,975.23 $ 2,500.00 $ 50,000.00 $ 3,975.23 - 2 $ 50,000.00 $ 6,475.23 $ 3,975.23 $ 2,500.00 $ 50,000.00 $ 8,188.97 238.51 3 $ 50,000.00 $ 6,475.23 $ 3,975.23 $ 2,500.00 $ 50,000.00 $ 12,655.54 491.34 4 $ 50,000.00 $ 6,475.23 $ 3,975.23 $ 2,500.00 $ 50,000.00 $ 17,390.10 759.33 5 $ 50,000.00 $ 6,475.23 $ 3,975.23 $ 2,500.00 $ 50,000.00 $ 22,408.73 1,043.41 6 $ 50,000.00 $ 6,475.23 $ 3,975.23 $ 2,500.00 $ 50,000.00 $ 27,728.49 1,344.52 7 $ 50,000.00 $ 6,475.23 $ 3,975.23 $ 2,500.00 $ 50,000.00 $ 33,367.42 1,663.71 8 $ 50,000.00 $ 6,475.23 $ 3,975.23 $ 2,500.00 $ 50,000.00 $ 39,344.70 2,002.05 9 $ 50,000.00 $ 6,475.23 $ 3,975.23 $ 2,500.00 $ 50,000.00 $ 45,680.61 2,360.68 10 $ 50,000.00 $ 6,475.23 $ 3,975.23 $ 2,500.00 $ 50,000.00 $ 52,396.67 2,740.84 $ 25,000.00 12,644.39 Annual cost = Interest = $ 2,500.00 (c ) Net amount of interest paid = Interest paid - interest earned on sinking fund (i) Amortization = Interest paid = $ 14,752.29 (ii) Sinking fund = Interest paid = $ 25,000.00 Less = Interest earned = 12,644.39 Net cost of loan 12,355.61 (d) Sinking fund balance before loan = $ 52,396.67 (From b) Less : Loan balance $ 50,000.00 Balance after payment of loan $ 2,396.67 Please provide feedback… Thanks in Advance :-)
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