25300 Chapter 4 & 5: TVM II
Tutorial questions 25300 FBF
Tutorial 3 – Time Value of Money 2
1. Aunty Helen is committed to saving $200 a month. How much would she have accumulated after
10 years if she saved the money in a bonus-interest account paying 4.8% p.a. compounding
monthly? What is the present value of this series of cash flows?
2. Gabrielle has just won the state lottery. She is given the choice of receiving a total of $1.5 million
now or she can elect to be paid $50,000 every six months for the next 20 years. If Gabrielle can earn
4% p.a. compounded semi-annually on her investments, from a strict economic point of view which
option should she choose?
3. Which annuity has a higher future value in the year 2030 if interest rates are 5% p.a.?
(a) $800 at the end of each year from 2017 to 2022, or
(b) $500 at the end of each year from 2019 to 2030?
4. How much do you have to deposit today so that you can make withdrawals of $4,000 a quarter with
the first withdrawal occurring in exactly eleven years and the final withdrawal occurring in exactly
thirteen years’ time. Assume an interest rate of 6% p.a. compounding quarterly.
5. With an 8% p.a. interest rate, calculate the present value of the following streams of payments:
(a) $1200 per year forever, with the first payment in one year’s time
(b) $1200 per year forever, with the first payment occurring five years from today
6. Lucy and Malcolm purchase a $700,000 house by paying a $250,000 deposit and borrowing the
balance. Their loan will be repaid with monthly payments over a twenty-year term at a rate of 6%
p.a. compounding monthly.
(a) What is the size of each repayment?
(b) Complete the loan amortisation schedule for the first two months.
(c) After two months, the interest rate on their variable rate loan increases to 6.60% p.a.
compounding monthly. What will their new monthly repayment be?
7. You are a financial planner and a client wishes to plan for her future. She wants to structure her
retirement so that she will receive twenty payments of $120,000 each year with the first $120,000
payment to be received on 11 August 2029.
You recommend that she make a series of annual equal-sized deposits into her superannuation
fund. The first deposit will be made on 11 August 2017 and the final deposit will be on 11 August
2028. The superannuation fund earns a constant return of 8% p.a.
What is the amount of the equal-sized deposits that she must make into her superannuation fund?
(Answers: 1. $30,726.39; $19,031.19, 2. $1.5m today, 3. (a), 4. $17,630.04, 5. (a) $15,000, (b) $11,025.45, 6. (a)
$3,223.94, (b) closing principal of $448,047.30, (c) $3,380.61, 7. $62,084.09)
