Final answer:
To have $10,000 in ten years with 10% interest compounded annually, you need to invest approximately $3,853.11
Step-by-step explanation:
To calculate the amount of money you need to invest in an account to have $10,000 in ten years with 10% interest compounded annually, you can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
- A is the future value (in this case, $10,000)
- P is the principal amount (what you need to calculate)
- r is the annual interest rate (in decimal form, 0.10)
- n is the number of times interest is compounded per year (in this case, 1)
- t is the number of years (in this case, 10)
Substituting the known values into the formula:
10,000 = P(1 + 0.10/1)^(1*10)
10,000 = P(1.10)^10
Dividing both sides of the equation by (1.10)^10:
P = 10,000 / (1.10)^10
Using a calculator, the approximate value of P is $3,853.11