All the sums require application of Future Value formula 3a). Yearly payment (PM
ID: 2644218 • Letter: A
Question
All the sums require application of Future Value formula 3a). Yearly payment (PMT) = $ 3600, I = 10% ie 0.10%, n = 40 years, FV = ? formula = FV = PMT [ ( ( 1 + i )^n -1 ) / i ] Fv = 3600 [ ( ( 1 + 0.10 )^40 -1 ) /0.10 ] $1,593,333 3b) PMT 3600 ; I - 6% = 0.06%, n = 40 years, FV = ? FV = PMT [ ( ( 1 + i )^n -1 ) / i ] Fv = 3600 [ ( ( 1 + 0.06) )^40 -1 ) /0.06 ] = $ 557,143 3c)Therefore, risk aversion and being too cautious All the sums require application of Future Value formula 3a). Yearly payment (PMT) = $ 3600, I = 10% ie 0.10%, n = 40 years, FV = ? formula = FV = PMT [ ( ( 1 + i )^n -1 ) / i ] Fv = 3600 [ ( ( 1 + 0.10 )^40 -1 ) /0.10 ] $1,593,333 3b) PMT 3600 ; I - 6% = 0.06%, n = 40 years, FV = ? FV = PMT [ ( ( 1 + i )^n -1 ) / i ] Fv = 3600 [ ( ( 1 + 0.06) )^40 -1 ) /0.06 ] = $ 557,143 3c)Therefore, risk aversion and being too cautiousExplanation / Answer
4a. The questions requires us to find the present value of $1,593,333 using inflation rate of 3% and interest rate of 10%. Using multiplicative model, the discount rate becomes 1.10 x 1.03 = 1.133 = 13.3%
Present value = Amount / (1+ i )n
Hence, we get: PV = 1,593,333 / (1.133)40 = 1593333 / 147.6374 = $10,792 approx.
4b. In this sub part, discount factor for calculating Present value will be: Inflation factor x Interest rate factor
i.e. 1.06 x 1.03 = 1.0918 = 9.18%
PV = Amount / (1+ i)n
Hence P.V. = 557143 / (1.0918)40 = 557143 / 33.5524 = $16,605 approx.
4c. $16,605 - $10792 = $5,813
This is the difference due to different risk aversion levels in 4a and 4b.