redeemed with a 216 payment annuity immediate so that the balance is 216 e 05

# Redeemed with a 216 payment annuity immediate so that

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redeemed with a 216-payment annuity-immediate so that the balance is   216 e 0 05 12 = 2,639.82 × 142 241 = \$ 375,490 7 By the retrospective method, the balance is 400,000 μ 1 + 0 05 12 24 2,639 24 e 0 05 12 = 441,976.53 2,639.82 × 25 186 = \$ 375,490 Hence, the two methods give the same answer. After the increase in the rate of interest, if the loan is to be repaid within the same period, the revised monthly installment is 375,490 216 e 0 055 12 = 375,490 136 927 = \$ 2,742.26 so that the increase in installment is \$102.44. Let be the remaining number of installments if the amount of installment remained unchanged. Thus, e 0 055 12 = 216 e 0 05 12 = 142 241 8 from which we solve for = 230 88 231 . Thus, it takes 15 months more to pay back the loan. 2 Example 5.2: A housing loan is to be repaid with a 15-year monthly annuity-immediate of \$2,000 at a nominal rate of 6% per year. After 20 payments, the borrower requests for the installments to be stopped for 12 months. Calculate the revised installment when the borrower starts to pay back again, so that the loan period remains unchanged. What is the di ff erence in the interest paid due to the temporary stoppage of installments? Solution: The loan is to be repaid over 15 × 12 = 180 payments. After 20 payments, the loan still has 160 installments to be paid. Using the prospective method, the balance of the loan after 20 payments is 2,000 × 160 e 0 005 = \$ 219,910 9 Note that if we calculate the loan balance using the retrospective method, we need to compute the original loan amount. The full calculation using the retrospective method is 2,000 180 e 0 005 (1 005) 20 2,000 20 e 0 005 = 2,000 (130 934 20 979) = \$ 219,910 Due to the delay in payments, the loan balance 12 months after the 20th payment is 219,910 (1 005) 12 = \$ 233,473 which has to be repaid with a 148-payment annuity-immediate. Hence, the revised installment is 233,473 148 e 0 005 = 233,473 104 401 = \$ 2,236.31 10 The di ff erence in the interest paid is 2,236.31 × 148 2,000 × 160 = \$ 10,973 2 Example 5.3: A man borrows a housing loan of \$500,000 from Bank A to be repaid by monthly installments over 20 years at nominal rate of interest of 4% per year. After 24 installments Bank B o ff ers the man a loan at rate of interest of 3.5% to be repaid over the same period. However, if the man wants to re- fi nance the loan he has to pay Bank A a penalty equal to 1.5% of the outstanding balance. If there are no other re- fi nancing costs, should the man re- fi nance the loan? 11 Solution: The monthly installment paid to Bank A is 500,000 240 e 0 04 12 = 500,000 165 02 = \$ 3,029.94 The outstanding balance after paying the 24th installment is 3,029.94 216 e 0 04 12 = 3,029.94 × 153 80 = \$ 466,004 If the man re- fi nances with Bank B, he needs to borrow 466,004 × 1 015 = \$ 472,994 so that the monthly installment is 472,994 216 e 0 035 12 = 472,994 160 09 = \$ 2,954.56 12 As this is less than the installments of \$3,029.94 he pays to Bank A, he should re- fi nance. 2 13 5.2 Amortization If a loan is repaid by the amortization method, each installment is fi rst used to o ff set the interest incurred since the last payment.  #### You've reached the end of your free preview.

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• Spring '17
• Tse Yiu Kuen
• Debt, Interest, Mortgage loan, Sinking Fund
• • • 