ENSC 201 Quiz, Sep 24 2010

Calculators may be used. Unless otherwise stated, all problems are set in Canada in 2010.

1) A bank advertises that it offers an interest rate of 5.5% per quarter, compounded

every two years. What effective annual interest rate is this equivalent to?

a) 12% b) 20% c) 24% d) 25% 5.5% per quarter is 44% per two-year period, so the effective two-yearly rate is 44%. To get the effective annual rate, j, we use the equation (1+j)2 = 1.44, hence 1+j = 1.2

2) Our interest rate is i%. We want to set aside a fixed amount $A every year to pay for

the purchase, in N years, of a machine that will cost $F. The size of A can be calculated from the formula:

a) F(F/A,i,N) b) F(A/F,i,N) c) F(P/F,i,N) d) F/(iN)

3) On September 24, 2010, I am promised a series of N payments of $A, the first one to be made at once, subsequent payments every September 24. If my interest rate is i, the present value of this series of payments is:

a) A + A(P/A,i,(N-1)) b) A(P/A,i,N) c) A + A(P/A,i,N) d) AN/i

As given, the pattern of payments doesn’t quite match the standard definition of an annuity – annuities are supposed to start in Year 1, not Year 0. So we treat the first payment separately and the remaining N-1 payments as an annuity.

4) On the birth of a child, a generous uncle offers to put the child’s age, in dollars, into a

bank account bearing interest at i% at every one of the child’s birthdays, starting with its first birthday in a year’s time and finishing with the child’s eighteenth birthday in eighteen year’s time. After the final deposit, the amount in the account will be:

a) (A/G,i,18) b) (A/G,i,18)(F/A,i,18) c) (A/G,i,18) )(F/A,i,18)(P/F,i,1) d) (A/G,i,18) )(F/A,i,18)(F/P,i,1)

Unfortunately, all the answers given here and my in-class `explanation’ were wrong. It’s actually much simpler than that. The pattern of payments is an arithmetic gradient, and the standard pattern for an arithmetic gradient is a series of N-1 payments, starting with a payment of G in Year 2 and finishing with a payment of (N-1)G in Year N. We can make this series fit this pattern by taking G = $1 and N = 19. If we do this, it turns out that the child is 1 year old in Year 2 and 18 years old in Year 19. This is a bit confusing, but the interest tables don’t really care about how old the child is. So the equivalent annuity is A = G(A/G,i,19), and the future sum equivalent to this annuity is F = A(F/A,i,19). Thus the right answer should have been F = (F/A,i,19)(A/G,i,19)

5) A project involves an initial outlay of $500, and yields a return of $605 after two

years. On the other hand, if I put my money in the bank, I can get an interest rate of i. What is the highest value of i at which I should choose to do the project rather than leave my money in the bank?

a) 10% b) 11% c) 20% d) 21% You can either solve this using the formulas at the end of the paper or the equation F=P(1+i)2

6) You have $1,000 to invest, and have two opportunities available. The first is to put

$500 into Project A; this will yield $600 after a year. The second is to put $800 into Project B; this will yield $900 after a year. You can also put money into the bank, where it will earn 10% interest, or borrow money from the bank at 11% interest. What is your most profitable strategy?

a) Put $500 in Project A and the rest in the bank b) Put $800 in Project B and the rest in the bank c) Put all $1000 in the bank. d) Borrow $300 from the bank and do both A and B Just calculate how much money each option gives you after a year and choose the highest figure.

7) Our interest rate is i%. We want to calculate the present value of a series of annual

payments of $A to us, starting in a year’s time and going on forever. This is given by:

a) The present value is infinite b) A(i + i2 + i3 + …) c) Ai d) A/i

8) We are considering four possible projects, W, X, Y, and Z. If we do W, we cannot do

Z. We cannot do Y unless we do W. The initial investments required for the projects are $100, $150, $200 and $250 respectively. If we have $400 to invest, what are the feasible sets of projects?

a) W, X, Z, {W, X}, {W, Y} b) W, X, Z, {W, Y}, {X,Y}, {X, Z} c) W, X, Z, {X,Y}, {X, Z}, {W, X, Y} d) W, X, Z, {X, Y}, {X, Z}

9) In the previous question, if the paybacks on each of the projects after one year are

$115, $165, $240, and $300 respectively, and if we can earn 12% by putting money in the bank, which projects are worth doing?

a) W and Z b) W, X and Z c) W, Y and Z d) X, Y and Z Calculate the value of i for each project and reject those with i < 12%

10) In the previous question, which project or combination of projects should we choose?

a) W and X b) W and Y c) Z d) X and Y

11) If the nominal interest rate offered by a bank is 12% per year, compounded monthly, then the effective annual interest rate is:

a) (1+0.12)12 - 1 b) 1% c) (1+0.01)12 - 1 d) (1-0.12)12 + 1

12) We are promised a payment of $100 in two years time, followed by payments of $200, $300 and $500 for the following three years, respectively. The present worth of this series of payments is

a) $100(A/G,i,5)(P/A,i,5) + $100(P/F,i,5) b) $100(A/G,i,4)(P/A,i,4) + $100(P/F,i,5) c) $100(A/G,i,4)(P/A,i,4)(P/F,i,1) + $100(P/F,i,5) d) $100(A/G,i,3)(P/A,i,3) + $100(P/F,i,4)