Math 1090
Quiz 6
April 20, 2015
Answer the following questions in the space provided. Time: 15 minutes
Name:
UID:
1. Suppose you invest a fixed amount $1, 000 at the end of each year for 3 years in an
account that pays 10% compounded annually.
(a) How much does each of the $1, 000 contribute to the final value of the account?
• Fist $1, 000:
• Second $1, 000:
• Third $1, 000:
3 −1
(b) After 3 years, the value of the account is 1000 (1+0.1)
0.1
your answers in (a)?
. How does this follow from
2. A lottery prize worth $1, 800, 000 is awarded in payments of $10, 000 at the beginning
of each month for 15 years. Suppose money is worth 6.6% monthly.
(a) What formula will you use to compute the real value the prize (today)?
(b) What does every parameter mean in that formula?
(c) What is the real value of the prize? (You don’t need to use your calculator: it
suffices to write down the expression that you would type).
Formulas
n
−1
i If a1 , a2 · · · is a geometric sequence where at = dat−1 , a1 + a2 + · · · + an = a1 dd−1
.
ii Simple interest: S = P (1 + rt).
r nt
iii Compound interest: R = P 1 + n
.
r n
r
iv AP Y = 1 + n
− 1 or AP Y = e − 1.
R((1+rc )N −1)
r
v Future value of an ordinary annuity S =
, where rc = n
, N = nt.
rc
h
i
N +1
(1+rc )
−1
r
vi Future value of an annuity due: S = R
− R, where rc = n
, N = nt.
r
c
vii Present value of an ordinary annuity: S =
R(1−(1+rc )−N )
,
rc
−N
viii Present value of an annuity due: S =
R(1+rc )(1−(1+rc )
rc
Page 2
)
where rc =
r
,
n
, where rc =
N = nt.
r
,
n
N = nt.