Question

how much will an initial investment of $1,000 earning interest of 8% a year be worth at the end of 20 years? how does this change if the interest is paid more frequently?

Answer 1

The value of an initial investment of $1,000 earning 8% interest per year at the end of 20 years is $4,661.38 with yearly compounding and $4,682.37 with quarterly compounding.

Step-by-step explanation:

To calculate the value of an initial investment earning compound interest, you can use the formula: A = P(1 + r/n)^(nt), where A is the future value, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the initial investment is $1,000, the interest rate is 8% (or 0.08), and the number of years is 20.

1. For yearly compounding, n = 1. Substitute the values into the formula: A = 1000(1 + 0.08/1)^(1*20) = $4,661.38
2. For more frequent compounding, let's say quarterly (n = 4). Substitute the values into the formula: A = 1000(1 + 0.08/4)^(4*20) = $4,682.37

So, the initial investment of $1,000 will be worth $4,661.38 at the end of 20 years with yearly compounding, and $4,682.37 with quarterly compounding.