Answer:
Step-by-step explanation:
Since we have an amount in the future of 750, we are going to use Future value formula; FV = PV (1+r)^t
where PV= Initial amount deposited
r= interest rate or discount rate
t = total duration of the investment
FV= 750
PV=500
r = 2.5% or 0.025 as a decimal
t = ?
Next, plug in the numbers into the formula;
750 = 500* (1+0.025)^t
divide both sides by 500;
750/500 = 1.025^t
Introduce <em>ln</em> on both sides
ln 1.5 = ln 
ln 1.5 = t ln 1.025
0.4054651 = 0.0246926 t
Divide both sides by 0.0246926 to solve for t;
0.4054651/0.0246926 = t
t = 16.42
Therefore it will take 16.42 years
Answer: 4/9
Step-by-step explanation:
The probability that annie picks a duck Pt= the probability of picking a duck without accounting for the added one (Po)+ probability of picking the added bird and it's a duck(Pi)
Pt = Po+Pi
Since the total number of birds in the right pond is 10 after the addition of one by john
Po= 4/10
Pi= the of john adding a duck × the probability of annie picking the added bird
Pi= 4/9 × 1/10
Pi = 4/90
Pt= 4/10 + 4/90
Pt = (36+4)/90
Pt=40/90
Pt= 4/9
(This implies that the probability of picking a duck remain the same even after the addition of one bird from the left ponds because they both have equal proportions of duck and geese i.e the initial number of duck and geese in both right and left ponds are 4 and 5 respectively)
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