Question

3. A scholarship fund is started on January 1, 2015 with an initial deposit of of $100,000 in an account earning i(2) = 0.08, with interest credited every June 30 and Dec 31. Every Jan. 1 from 2016 on, the fund will receive a deposit of $5,000. The scholarship fund makes payments to recipients totaling $12,000 every July 1, starting in 2015. What amount is in the scholarship account just after the $5,000 deposit is made on Jan 1, 2025? Hint: (i) What is the annual effective interest rate? What is the 6-month rate? (ii) How long is the period from the initial deposit of $100,000 until (iii) To what do the annual deposits of $5000 grow by Jan 1, 2025? (iii) To what would the annual withdrawals have grown by Jan 1, 2025? (Note that they're made midyear.) ANS: $109,926.03

Answer 1

On Januany 1, 2015 the account balance is 100,000 In account balance June 30, 2015 - 6 month rate 100 000 + 100 000X 08 = 204 X 100 000 on July 2, 2015 account balance is 109x100 000 - 12000 On Dec 31, 2015 account balance is (104 * 10000 - 12000 )* (1 + 0 2 95680 =P (say). is Now On accountabalance Jan 1, 2016 is On Pt 5000 Jun 30 2016 account balance (P + 5000 ) & (14.09) July 1, 2016 account kalance (p+ 5000 ) x 109 - 12000 is On on Dec 31, 2016 account balance is ((P+ 5000) * 109 -12000 ) *(1+.09) (1.09) ? – (109) & 6800 P' (says -

similanly, on Dec 31, 2017 the account balance is p" = non 2 pl -1.04x6800 = (1043² [ (lion) ²p - (1109) +6800] -1.094.6800 = (1.ga 4 p - proceeding in 6800 5 1009+ (1104)3 ] this way, the accoun balance will be On Dec 31, 2029 2x9-17 2X9 3 S = (1-04) P - 6800 T 10q+ 104'*-- +1.04 18 - (109) P 1.04 -1 6800 x 1.04" - riog27 - Now, account will 104926:03 [ putting value of A After the deposit of 5000 the balance with be on Jan 1, 2025 be (109926.03+ 5000) 10992603