saab bank saab bank saab bank Problem 2 SAAB Bank lent a newly graduated enginee
ID: 2791115 • Letter: S
Question
saab bank saab bank saab bank Problem 2 SAAB Bank lent a newly graduated engineer $ 2000 at 1-8% per year for 5 years to buy home office furniture. From the bank's perspective (the lender), the investment in this young engineer is expected to produce an equivalent net cash flow of &315.47 for each of 5 years. A = $2000 (A/P, 890, 5) = $ This represents a 8% per year rate of return on the bank's unrecovered balance. Compute the amount of the unrecovered investment for each of the 4 years using: a- The rate of return on the unrecovered balance (correct basis). b- The return on the initial $2000 investment. c- Explain why all the initial $2000 amount is not recovered by the final payment in part (b).Explanation / Answer
Investment amortisation with annuity of $ 315.47 Year Annual payment Tow.int. Tow.principal Unrecovered investment at end of each year -ie. Principal balance 0 2000 1 315.47 160 155.47 1844.53 2 315.47 147.56 167.91 1676.62 3 315.47 134.13 181.34 1495.28 4 315.47 119.62 195.85 1299.43 5 315.47 103.95 211.52 1087.92 1577.35 665.27 912.08 The equal yearly annuity at 8% for 5 years ,to repay the 2000 comes to: Using the PV of annuity formula, 2000=Pmt.*(1-1.08^-5)/0.08 500.91 Thus the recovery of $ 315.47 is less than 500.91 found out above--hence the $ 2000 is still not recovered by the end of year 5 When the annual annuity is $ 500.91, the entire investment,by the bank is recovered. Investment amortisation with annuity of $ 500.91 Year Annual payment Tow.int. Tow.principal Unrecovered investment at end of each year -ie. Principal balance 0 2000 1 500.91 160 340.91 1659.09 2 500.91 132.73 368.18 1290.91 3 500.91 103.27 397.64 893.27 4 500.91 71.46 429.45 463.82 5 500.91 37.11 463.80 0.02 2504.55 504.57 1999.98 There is short-recovery of 500.91-315.47= $ 185.44 by the bank,which is why the $ 2000 investment is not fully recovered at end of yr. 5
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