I only need the explanation for all parts of part b Your brother has offered to
ID: 2382765 • Letter: I
Question
I only need the explanation for all parts of part b
Your brother has offered to give you 20 annual payments, starting at $ 110 next year, and after that growing at 3.3% per year. You would like to calculate the value of this offer by calculating how much money you would need to deposit in a local bank so that the amount will generate the same cash flows as he is offering you. Your local bank will guarantee a 5.6% annual interest rate so long as you have money in the account. a. How much money will you need to deposit into the account today so that the account will generate the same cash flows as he is offering you? b. Assuming you deposited the amount of money in part (a), and then withdrew the required payments each year, calculate the remaining balance at the end of years 1, 2, 10 and 19. (Hint: To solve this problem it is best to use an excel spreadsheet.)Explanation / Answer
Initial payment 110 Annual growth rate 3.30% Number of periods 20 Discount rate 5.60% a. Money will you will need to deposit into the account today will be the PV of growing annuity (using the formula) P/r-g [ 1 - {1+g/1+r}^n] where P = first payment, r = rate per period n = no of periods, g = growth rate subsituting the values we get 1703.73 Excel spreadsheet, showing the details of nterest earned, amount paid and balance amount remaining at the end of the period. Opening Balance (1) interest for the year @ 5.6% * op balance (2) Amount paid out end of year with 3.3 growth over the previous year (3) ending balance (1+2-3) 1 1,703.73 95.41 110 1,689.14 2 1,689.14 94.59 113.63 1,670.10 3 1,670.10 93.53 117.38 1,646.25 4 1,646.25 92.19 121.25 1,617.18 5 1,617.18 90.56 125.25 1,582.49 6 1,582.49 88.62 129.39 1,541.72 7 1,541.72 86.34 133.66 1,494.40 8 1,494.40 83.69 138.07 1,440.02 9 1,440.02 80.64 142.62 1,378.03 10 1,378.03 77.17 147.33 1,307.87 11 1,307.87 73.24 152.19 1,228.92 12 1,228.92 68.82 157.22 1,140.52 13 1,140.52 63.87 162.4 1,041.99 14 1,041.99 58.35 167.76 932.58 15 932.58 52.22 173.3 811.50 16 811.50 45.44 179.02 677.93 17 677.93 37.96 184.93 530.97 18 530.97 29.73 191.03 369.67 19 369.67 20.70 197.33 193.04 20 193.04 10.81 203.84 0.01 Reading from the above table, balance remaining at the end of Year Amount 1 1689.14 2 1670.10 10 1307.87 19 193.04