COMPOUND INTEREST INVESTMENTS WITH REGULAR ADDITIONS TO THE PRINCIPAL These are INVESTMENTS where you speed up the way your investment grows by adding extra regular amounts to the investment each compounding period. Vn = value of the investment after n compounding The recurrence relation for the value of the periods. investment after n compounding periods is: r = interest rate (per compounding period) V0 = principal and Vn+1 = R Vn + D D = regular addition to the principal Where When using the Finance Solver, the value entered for Pmt is NEGATIVE because this is an amount adding to the principal. Andrew is aged 45 and is planning to retire at 65 years of age. He estimates that he needs $480 000 to provide for his retirement. His current superannuation fund has a balance of $60 000 and is delivering 7% pa, compounded monthly. (a) Find the monthly contributions needed to meet the retirement lump sum target (b) If in the final ten years before retirement, Andrew doubles his monthly contribution calculated from (a), find the new lump sum amount available for retirement. (c) How much extra could Andrew expect if the interest rate from part (b) is increased to 9% p.a. for the final ten years compounded monthly? Round your answer to the nearest $1000. (a) $456.26 (b) $558 974.01 (c) $665.757.29 $558974.01 = $107 000 extra – (to the nearest $1000) first ten years next ten years N = 20 * 12 = 240 N = 120 N = 120 N = 20 * 12 = 240 I = 7 I = 7 I = 7 I = 9 PV = -60 000 PV = -60 000 PV = -199 551.36 PV = -199 551.36 Pmt = $456.26 Pmt = 456.26 Pmt = 456.26*2 Pmt = 456.26*2 FV = 480 000 FV = $199 551.36 FV = $558 974.01 FV = $665 757.29 Ppy = Ppy = Ppy = Ppy = 12 12 12 12 Cpy = 12 Cpy = 12 Cpy = 12 Cpy = 12 PmtAt END PmtAt END PmtAt END PmtAt END Now try ex 9F
COMPOUND INTEREST INVESTMENTS WITH REGULAR ADDITIONS TO THE PRINCIPAL These are INVESTMENTS where you speed up the way your investment grows by adding extra regular amounts to the investment each compounding period. Vn = value of the investment after n compounding periods. r = interest rate (per compounding period) D = regular addition to the principal The recurrence relation for the value of the investment after n compounding periods is: V0 = principal and Vn+1 = R Vn + D Where When using the Finance Solver, the value entered for Pmt is NEGATIVE because this is an amount adding to the principal. Andrew is aged 45 and is planning to retire at 65 years of age. He estimates that he needs $480 000 to provide for his retirement. His current superannuation fund has a balance of $60 000 and is delivering 7% pa, compounded monthly. (a) Find the monthly contributions needed to meet the retirement lump sum target (b) If in the final ten years before retirement, Andrew doubles his monthly contribution calculated from (a), find the new lump sum amount available for retirement. (c) How much extra could Andrew expect if the interest rate from part (b) is increased to 9% p.a. for the final ten years compounded monthly? Round your answer to the nearest $1000. (a) $456.26 (b) $558 974.01 (c) $665.757.29 – $558974.01 = $107 000 extra (to the nearest $1000) first ten years next ten years N = 20 * 12 = 240 I = 7 PV = -60 000 Pmt = $456.26 FV = 480 000 Ppy = 12 Cpy = 12 PmtAt END N = 120 I = 7 PV = -60 000 Pmt = 456.26 FV = $199 551.36 Ppy = 12 Cpy = 12 PmtAt END N = 120 I = 7 PV = -199 551.36 Pmt = 456.26*2 FV = $558 974.01 Ppy = 12 Cpy = 12 PmtAt END N = 20 * 12 = 240 I = 9 PV = -199 551.36 Pmt = 456.26*2 FV = $665 757.29 Ppy = 12 Cpy = 12 PmtAt END Now try ex 9F
Investments-with-additions-filled-in.docx