Answer: the value of her investment after 4 years is £8934.3
Step-by-step explanation:
The formula for determining compound interest is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount invested.
t represents the duration of the investment in years.
From the information given,
P = 8000
r = 2.8% = 2.8/100 = 0.028
n = 1 because it was compounded once in a year.
t = 4 years
Therefore,
A = 8000(1+0.028/1)^1 × 4
A = 8000(1+0.028)^4
A = 8000(1.028)^4
A = £8934.3 to the the nearest penny
Let Joy be x years old
<span>Joy's brother's age is 3 years older than twice joy's age.
</span>Joy's Brother = 2x + 3
<span>The sum of Joy's age and her brother's age is 24.
x + 2x + 3 = 24
3x + 3 = 24
3x = 24 - 3
3x = 21
x = 21 </span>÷ 3
x = 7
Joy:
x = 7
Brother:
2x + 3 = 2(7) + 3 = 17
Difference in their age = 17 - 7 = 10 years
They are 10 years apart.
Answer:
Alternative form: 0.25(1-3x)
<span>let x = the original no. of students
then
(x+10) = the actual no. that went on the trip
:
= the original cost per student
and
= the actual cost
:
Original cost - actual cost = $12.50
- = 12.50
multiply equation by x(x+10)
x(x+10)* - x(x+10)* = 12.50x(x+10)
Cancel the denominators
1500(x+10) - 1500x = 12.5x(x+10)
1500x + 15000 - 1500x = 12.5x^2 + 125x
Combine on the right to form a quadratic equation
0 = 12.5x^2 + 125x - 15000
Simplify, divide equation by 12.5
x^2 + 10x - 1200 = 0
You can use the quadratic formula; a=1; b=10; c=-1200, but this will factor to
(x + 40(x - 30) = 0
The positive solution is what we want here
x = 30 students in the original group
Check this by finding the cost per student for each scenario
1500/30 = $50.00; original cost
1500/40 = $37.50; actual cost
---------------------
saving: $12.50</span>
