Answer:
When using formulas in application, or memorizing them for tests, it is helpful to note the similarities and differences in the formulas so you don’t mix them up. Compare the formulas for savings annuities vs payout annuities.
Savings Annuity Payout Annuity
P
N
=
d
(
(
1
+
r
k
)
N
k
−
1
)
(
r
k
)
P
0
=
d
(
1
−
(
1
+
r
k
)
−
N
k
)
(
r
k
)
PAYOUT ANNUITY FORMULA
P
0
=
d
(
1
−
(
1
+
r
k
)
−
N
k
)
(
r
k
)
P0 is the balance in the account at the beginning (starting amount, or principal).
d is the regular withdrawal (the amount you take out each year, each month, etc.)
r is the annual interest rate (in decimal form. Example: 5% = 0.05)
k is the number of compounding periods in one year.
N is the number of years we plan to take withdrawals
A 5% discount indicates that her total purchase amount will be decreased by 5%. Paying full price could be shown as 1.00, so we must subtract 0.05 from the full price to represent the discounted total (1.00-0.05 = 0.95).
Only one choice, D, contains this multiplier so we can be certain of this answer.
F(x) is continuous for all x.
Pick a point and show that f(x) is either negative or positive. Pick another point and show that f(x) is negative, if positive, or positive, if negative.
At x = 30, f(30) - 1000 = 900 + 10sin(30) - 1000 ≤ 0
Now, show at another point f(x) - 1000 is positive, and hence, there would be root between 30 and such point.
Let's pick 40.
At x = 40, f(40) - 1000 = 1600 + 10sin(40) - 1000 ≥ 0
Since f(x) - 1000 is continuous, there lies a root between 30 and 40, and hence, 30 ≤ c ≤ 40
What statement are you talking about?
