Calculate the compound interest on $1,000 at a rate of 5% for 3 years.

To calculate the compound interest earned on an investment, the formula used is:

[ A = P \left(1 + \frac{r}{n}\right)^{nt} ]

where:

• ( A ) is the amount of money accumulated after n years, including interest.

• ( P ) is the principal amount (initial investment).

• ( r ) is the annual nominal interest rate (decimal).

• ( n ) is the number of times that interest is compounded per year.

• ( t ) is the time the money is invested for in years.

In this scenario:

• The principal ( P = 1000 ).

• The nominal interest rate ( r = 0.05 ).

• Assuming that interest is compounded annually, ( n = 1 ).

• The time period ( t = 3 ).

Plugging in the values, we have:

[ A = 1000 \left(1 + \frac{0.05}{1}\right)^{1 \times 3} ]

[ A = 1000 \left(1 + 0.05\right)^{3} ]

[ A = 1000 \left(1.05\right