<span>B(n) = A(1 + i)^n - (P/i)[(1 + i)^n - 1]
where B is the balance after n payments are made, i is the monthly interest rate, P is the monthly payment and A is the initial amount of loan.
We require B(n) = 0...i.e. balance of 0 after n months.
so, 0 = A(1 + i)^n - (P/i)[(1 + i)^n - 1]
Then, with some algebraic juggling we get:
n = -[log(1 - (Ai/P)]/log(1 + i)
Now, payment is at the beginning of the month, so A = $754.43 - $150 => $604.43
Also, i = (13.6/100)/12 => 0.136/12 per month
i.e. n = -[log(1 - (604.43)(0.136/12)/150)]/log(1 + 0.136/12)
so, n = 4.15 months...i.e. 4 payments + remainder
b) Now we have A = $754.43 - $300 = $454.43 so,
n = -[log(1 - (454.43)(0.136/12)/300)]/log(1 + 0.136/12)
so, n = 1.54 months...i.e. 1 payment + remainder
</span>
Answer:
26.2% of smokers,when given this treatment, would refrain from smoking for at least 6 months.
Step-by-step explanation:
In this problem, we have that:
935 smokers received the treatment(nicotine patch).
After 6 months, 245 of them were not smoking.
Assuming it is reasonable to regard this sample as representative of all smokers, estimate the percentage of all smokers who, when given this treatment, would refrain from smoking for at least 6 months.
This percentage is 245/935 = 0.2620.
26% of smokers,when given this treatment, would refrain from smoking for at least 6 months.
Answer:
31 years to triple the investment
Step-by-step explanation:
Initial investment = 300
Triple amount that is final amount = 300*3= 900
rate of interest = 3.5 % = 0.035
we need to find out number of years (t)
for compounded continuously we use formula
A is the final amount
P is the initial amount
r is the rate of interest
t is the number of years
Divide both sides by 300
take 'ln' on both sides
ln(3) = 0.035t ln(e)
ln(e)= 1
t= 31.3889
Round to nearest whole number
t= 31 years
6 inches because 24 is 3 times greater than 8, so you would do 18/3.
Answer:
9(t+5)<6
t<-13/3
Step-by-step explanation:
The expression is 9(t+5)<6
Distributing the 9, we get
9t+45<6
9t<-39
t<-13/3
