To determine the future value of an investment, we can use the formula for compound interest:
Formula:
A = P(1 + r/n)^(nt)
Where:
- A = the future value of the investment/loan, including interest
- P = the principal investment amount ($5,000)
- r = annual interest rate (decimal) (10% or 0.10)
- n = number of times that interest is compounded per year (1 for annually)
- t = the number of years the money is invested for (10 years)
Plugging in the values:
A = 5000(1 + 0.10/1)^(1*10)
A = 5000(1 + 0.10)^10
A = 5000(1.10)^10
A = 5000 * 2.5937424601
A = 12,968.71
So, the investment of $5,000 at a 10% annual interest rate compounded annually will grow to approximately $12,968.71 in 10 years.