investment of 2000 doubles every 8 years. how much is the investment worth after 24 years. after 32 years.
To determine the worth of an investment after a certain number of years, we can use the compounded interest formula:
A = P * (1 + r/n)^(n*t)
Where:
A = the final amount after t years
P = the initial investment amount
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, we know that the initial investment is $2000, and it doubles every 8 years. This indicates that the interest rate is 100% divided by 8, or 12.5% per year. Since the investment doubles, n can be assumed to be 1 (compounded annually).
Let's calculate the worth of the investment after 24 and 32 years:
For 24 years:
A = 2000 * (1 + 0.125/1)^(1*24)
A = 2000 * (1 + 0.125)^24
A ≈ $16,000
So, the investment is worth approximately $16,000 after 24 years.
For 32 years:
A = 2000 * (1 + 0.125/1)^(1*32)
A = 2000 * (1 + 0.125)^32
A ≈ $32,000
Therefore, the investment is worth approximately $32,000 after 32 years.
24 = 8*3, so it will have doubled 3 times
similarly for 32 = 8*4
n = 24/8 = 3
V = 2^n * Vo = 2^3 * 2000 = $16,000.
n = 32/8 = 4
V = 2^n * Vo = 2^4 * 2000 =