Answer:
a. $4.48¢
b. 9,967 people
ci. Multiplier: F = 25 × (1.09)^t
cii. Percent increase = 9.15%
Step-by-step explanation:
a. The equation we are going to use to calculate the future cost of bread in 5 years:
P = F/(1+r)^t
Where P is current cost, F = future cost(what we are required to calculate), r = percentage increase per year, t = time (years).
Where P = 2.75
r = 5/100 or 0.05
t = 10
F = ?
Substituting appropriately, we have:
2.75/1 = F/(1+0.05)^10
We then cross multiply
F = 2.75 × (1+0.05)^10
F = 2.75 × (1.05)^10
F = 2.75 × 1.62889
F = $4.48¢
Therefore, the bread will cost $4.48 in 10 years.
b. Here population is 42,000 people now. There's predicted 25% decrease in population every year for the next 5years. We are to calculate the expected population in 5 years. The equation that can be used to calculate the expected population:
P = F/(1 - r)^t
F = future population
P = present population
r = percentage of decrement
t = period.
Here P = 42,000
r = 25/100 = 0.25
t = 5
F = ?
Substituting accordingly:
42000 = F/(1 - 0.25)^5
Cross multiply
F = 42000 × [(1 - 0.25)^5]
F = 42000 × 0.2373
F = 9,967
The population in the next 5 years will decrease to 9,967 people.
c. Share of orange stock = $25 in the year 2000
The same share = $60 in 2010, we are required to determine the multiplier and percent increase.
Since the future value = $60, the present value = $25, the time = 2010 - 2000 = 10 years. Then we can use the formula:-
F = P × (1 + r)^t
60 = 25 × (1 + r)^10
(1 + r)^10 = 60/25
(1 + r)^10 = 2.4
1 + r = 10√2.4
1 + r = 1.0915
r = 1.0915 - 1
r = 0.0915
r = 9.15%
Therefore the multiplier is:
F = 25 × (1.09)^t
The percent increase = 9.15%
