Question

James plans to set up some savings for the higher education of his son, Jeffrey, who Just celebrates his 12th birthday today. Suppose Jeffrey will enroll in a 4-year bachelor course on his 19th birthday and the first-year tuition will be due on the same day. The remaining three tuitions will be paid on his 20th, 21st and 22nd birthdays. As of FY 2018/19, university tuition is, on average, $20,000 per annum (p.a.) as of FY 2018/19 and will grow by 2% p.a., i.e. the annual fee payable would be $20,000 x 1.02 = $20,400 for FY2019/20. After the enrolement, the annual tuition will be fixed across his four-year coursework study. James will make annual contributions to the saving account, starting from now. The last payment will be made on Jeffrey’s 21^st birthday. Since then, the account will cease operation. Assume the saving account is tax-free

1. Bank A offers 6.00% p.a. compounding annually, while Bank offers 5.76% p.a. compounding monthly. Which bank should James choose?

Below parts are based on your

decision in Part (a).

b. How much is the projected annual tuition fee when Jeffrey enrols in the university on his 19^th birthday? For simplicity, round the amount UP to the nearest thousand.

c. What is the minimum annual contribution James has to lodge into the saving account?

d. What is outstanding balance of the saving account on 1 Nov 2026? Demonstration using EXCEL spreadsheet is acceptable. If   James to contribute $13,000 annually to the account (starting from now), by which year Jeffrey’s higher education will be fully funded

Answer 1

1 1) Which bank interst rate is better bank A Other Bank Bank a interest rate is better option as the rate is more than the rate of other bank. 6% annulay 5.76% monthly compouded 6.00% 5.91% -(14(5.76%/12)712-1 No of years Fund required PMT 72) 2019-2012 2020-2012 20,000 $2,247.83 20,400 $1944.47 20,808 1708.26 21,224 1,519.08 9 2021-2012 2022-2012 Total 82.432 7,419.64 14 Annual minimum saving required is 7419.64 Accumulated value on 21st birthday 17 3) PMT $2,247.83 $1,944.47 $1,708.26 $1,519.08 $20,000.00 $17,300.82 $15,19.21 $13.515.94 23 Total 66,015.97 24 25 4) Future value if saving is done@13000 then balance as on 2026 is calculated below OP balance payment Closing bal 115,667.08 115,187.11 114.254.33 112,833.11 110,885.66 131,318.80 152,977.93 175,936.60 13000 20,000.00 13000 20,400.00 13000 20,808.00 13000 21,224.00 0.00 0.00 0.00 0.00 115,187.11 114.254.33 112,833.11 110,885.66 131318.80 152,977.93 175,936.60 27 2021 2022 2023 2024 2025 2026 13000 200,272.80 Balnace losing balance on 2026 will be 200273 37 years 39 5) Total fund required ment of 82432 will be fullfilled in the years 5.26 NPERIE6,13000.,-82432,1)

1) which bank interst rate is better bank A Other Bank Bank a interest rate is better opti 1 6% annulay 5.76% monthly compouded 0.06 s(1+5.76%/12)712-1-(14(5.76%/12)712-1 Fund required PMT 20000 =+07. 1.02 =PMT(E2,8,,-20400,1) -+D81.02 PMTIE2,9..-20808,1] -+091.02 PMTIE2,10..-21224,1) No of years PMTIE2.,7-20000,1) 72) 2019-2012 2020-2012 2021-2012 10 2022-2012 Total -SUMID7:011)SUM(E7:E11) Annual minimum saving req Accumulated value on 21st birthday 17 3) PMT =-E8 -+ES =-E10 -FVIE2,7,B20.,10 --FV(E2,7,B21..1) 20 Total -SUM(C18: C21) 24 25 4) Future value if saving is done @1: 26 OP balance --FVE2,7,13000 = +F27 +F28 +F29 -+F30 payment 20000 20400 20808 21224 Closing bal (C27+027-E27) 1.06 (C28+028-E28) 1.06 (C29+029-E29) 1.06 2019 2020 ,1) 13000 29 30 2022 312023 2024 2025 2026 C30+030-E30) 1.06 (C31+D31-E31 106 (C32+032-E32) 1.06 (C33+033-E33) 1.06 (C34+034-E34)' 1.06 32 +F32 +F33 13000 Balnace 34 35 36 balance on 2026 will years 39 5) Total fund required ment of 8243 ENPERIE2,13000,,-82432,1) -NPERIE6,13000,--82432,1〕