Question 2

Karine and Arlo are trying to establish a University Fund for their daughter Amelia, who turns 2 today.They plan for Amelia to withdraw $12,000 on her 18th birthday and $13,000, $14,000 and $15,000 on her subsequent birthdays (19th, 20th and 21st).They wish to deposit money into an account so that, with interest it will build up enough to make the planned withdrawals.They wish to make ten equal annual deposits, and they intend to make their first deposit one year from today, and expect to earn an average return of 6.55%pa on the account.

i) How much will Karine and Arlo have to deposit each year to the account to achieve their goal?

ii) Need a schedule showing the cash inflows (including interest) and outflows of this fund.How much will be in the fund on Amelia's 16th birthday?

I'M HAVING ISSUES WITH THE SCHEDULE. I AM FAIRLY SURE I HAVE PV10, THE PA DEPOSIT AND THE AMOUNT FOR 16TH BIRTHDAY CORRECT. I HAVE CHECKED WITH SOME OTHER STUDENTS AND HAVE GOT DIFFERENT RESULTS WHICH CONFUSE ME MORE. MY SPREADSHEET IS ATTACHED.

Question 2 Karine and Arlo are trying to establish a University Fund for their daughter Amelia, who turns 2 withdraw $12,000 on her 18th birthday and $13,000, $14,000 and $15,000 on her subsequent b wish to deposit money into an account so that, with interest it will build up enough to make the make ten equal annual deposits, and they intend to make their first deposit one year from toda return of 6.55%pa on the account. i) How much will Karine and Arlo have to deposit each year to the account to achieve their goal ii) Create a schedule showing the cash infows (including interest) and outlows of this fund. Ho Amelia's 16th birthday? *end of each year payment is made Yrs 0 1 Age 2 3 CF +CF +CF Withdraw 2 4 3 5 +CF 4 6 +CF 5 7 +CF 6 8 +CF 7 9 +CF 8 10 +CF 9 11 +CF Present Value Interest rate 0.0655 Term 10 Pv10 33440.98 pa deposit 2472.3033 Terms remaining to 16 Value at 16th Birthday Assuming interest rate is nominal, compounding per year, i = 0.0655 EAR = is the same as pa rate as the period is the same (1 year) 1) How much will Karine and Arlo have to deposit each year to the account to achieve their goal? Find the present values for birthdays 18,19,20 & 21 on the 10th year (Pv10) 12K/(1.0655)^6 + 12K/(1.0655)^7 + 12K/(1.0655)^8 + 12K/(1.0655)^9 = 33,206.1178 At the end of 10th year the PV is = 33,440.98 We will use the FV Annuity formula for the period of ten years (payments) rearranged to find the amount contributed annually for the 10 terms of payment: FV = C ((1+ ) ^1)/ FV = C ((1.0655)^101)/0.0655 So rearranging the formula to get C needs formatting C = 33,440.98 / ( 1.0655 ^101)/0.0655 C = $2472 2) How much will be in the fund on Amelia's 16 th birthday? From previous problem, we worked out that the Present Value in the account will be $33.206.12 by the end of 10th year. All contributions after this cease. What we need to do is use a compound interest rate formula based on Pv10 to find future value for period 14 (being Amelia's 16th birthday). FV = Pv10(1+i)^n We discount the periods to only count onwards from Pv10, so n = 4 FV14 = 33,440.98(1.0655)^4 FV14 = 43101.54 $43,102 will be in the fund on Amelia's 16th birthday. FV = Pv10(1+i)^n We discount the periods to only count onwards from Pv10, so n = 4 FV14 = 33,440.98(1.0655)^4 FV14 = 43101.54 $43,102 will be in the fund on Amelia's 16th birthday. er Amelia, who turns 2 today. They plan for Amelia to 0 on her subsequent birthdays (19 th, 20th and 21st). They up enough to make the planned withdrawals. They wish to osit one year from today, and expect to earn an average nt to achieve their goal? tlows of this fund. How much will be in the fund on 10 12 11 13 12 14 13 15 14 16 15 17 +CF 16 18 -CF 17 19 -CF 12000 13000 33440.977 Terms remaining to 16th birthday n = Value at 16th Birthday = goal? the amount contributed 6.12 by the end of 10th ormula based on Pv10 to 4 43102 Year Age 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Cash 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Interest 2472.30 2472.30 2472.30 2472.30 2472.30 2472.30 2472.30 2472.30 2472.30 2472.30 2472.30 2472.30 2472.30 2472.30 2472.30 2472.30 2472.30 2472.30 2472.30 Balance 161.94 334.48 518.32 714.21 922.93 1145.31 1382.27 1634.74 1903.75 2190.38 2495.79 2821.20 3167.92 3537.36 3930.99 4350.41 4011.30 3584.47 3064.19 2634.24 5441.02 8431.65 11618.16 15013.39 18631.00 22485.57 26592.62 30968.67 35631.36 40599.45 45892.96 51533.19 57542.85 63946.14 70768.86 65252.45 58309.23 49845.72 ' 18 20 -CF 19 21 -CF 14000 Withdrawas 15000 Final balance 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12000 13000 14000 15000 2634.24 5441.02 8431.65 11618.16 15013.39 18631.00 22485.57 26592.62 30968.67 35631.36 40599.45 45892.96 51533.19 57542.85 63946.14 58768.86 52252.45 44309.23 34845.72