Final answer:
To find the future value of a $1000 investment compounded at a 5% interest rate after 20 years, the calculations yield $2653.30 when compounded annually, $2719.64 when compounded monthly, and $2764.91 when compounded continuously.
Step-by-step explanation:
To find the value after 20 years of $1000 compounded at an interest rate of 5%, we need to use the formulas for compound interest for different compounding periods.
Compound Interest Annually
The formula for compound interest compounded annually is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
In this case, to calculate the amount when interest is compounded annually (n=1), we have:
A = 1000 * (1 + 0.05/1)^(1*20) = 1000 * (1.05)^20
After the calculation:
A = $2653.30
Compound Interest Monthly
When interest is compounded monthly (n=12), the formula is the same, but we adjust n:
A = 1000 * (1 + 0.05/12)^(12*20)
After the calculation:
A = $2719.64
Compound Interest Continuously
To calculate the amount when interest is compounded continuously, we use the formula:
A = Pe^(rt)
Where e is the base of the natural logarithms (~2.71828).
In this case:
A = 1000 * e^(0.05*20)
After the calculation:
A = $2764.91