Respuesta :
Answer:
In order to reach the target amount in 25 years with 5% interest we need to invest 87,282.8838 $.
Step-by-step explanation:
To find out the amount to be invested we can use the compound interest formula wich is given by:
A = P(1 + r/n)^(n*t)
Where A is the final amount, in our case we want to reach a value of $ 300,000.
P is the initial amount, this is what we want to find out.
r is the interest rate, it was given to us in the question that is 5% or 0.05
n is the number of compoundings a year, since it is semiannually we know n = 2
t is the total time for wich the money will be applied, t = 25 years.
Applying these values on the formula, we have:
300,000 = P(1 + 0.05/2)^(2*25)
300,000 = P(1 + 0.025)^(50)
300,000 = P(1.025)^(50)
300,000 = P(3.4371)
P*(3.4371) = 300,000
P = 300,000/3.4371 = 87,282.8838 $
In order to reach the target amount in 25 years with 5% interest we need to invest 87,282.8838 $.
Given Information:
Interest rate = r = 5%
Compounding semi-annually = n = 2
Accumulated amount = A = $300,000
Number of years = t = 25
Required Information
Semi-annually payment = P = ?
Answer:
Semi-annually payment ≈ $87,283
Step-by-step explanation:
Accumulated and principle amounts in terms of compound interest is given by
P = A/(1 + i)^N
Where
i = r/n = 0.05/2 = 0.025
N = n*t = 2*25 = 50
P = 300,000/(1 + 0.025)^50
P ≈ $87,283
Therefore, you need to invest $87,283 two times a year for 25 years to reach a savings goal of $300,000.
