Question but why a(i) the nis not 29 Question \( 2(20 \) marks) a) Carter expects to live for 30 years more after his retirement. He would like to withdraw \( \$ 120.000 \) every year from his investment account (Account A) to pay for his living expenses. Carter's investment account (Account A) pays \( 5 \% \) interest per year. How much money (a lump-sum) will Carter required to deposit in Account \( A \) at the beginning of his retirement (at age 60) to pay for his living expenses if (i) Account A start to pay interest one year after his retirement? \( \rightarrow \) aft c 15 marks) (ii) Account A start to pay interest on the day of his retirement? of eac ( marks) [Hint: The total deposit that Carter made at the beginning of his retirement in Account A should be the same as the amount required to provide for the monthly living expenses during his retirement years.]

【General guidance】The answer provided below has been developed in a clear step by step manner.Step1/2(i) To calculate the lump sum amount that Carter will require at the beginning of his retirement if Account A starts to pay interest one year after his retirement, we can use the formula for present value of an annuity:\( \mathrm{{P}{V}={A}\times{\left[\frac{{{1}-{\left({1}+{r}\right)}^{{-{{n}}}}}}{{r}}\right]}} \)where PV is the present value, A is the annual withdrawal amount, r is the interest rate per year, and n is the number of years of withdrawals.In this case, A = $120,000, r = 0.05, and n = 30. However, since Account A starts to pay interest one year after his retirement, we need to adjust n to 29.PV = \( \mathrm{\${120},{000}\times{\left[\frac{{{1}-{\left({1}+{0.05}\right)}^{{-{{29}}}}}}{{0.05}}\right]}} \)PV = $1,939,341.95Therefore, Carter will require a lump sum amount of $1,939,341.95 to deposit in Account A at ... See the full answer