Final answer:
To find the future value of $5000 invested at 4% interest compounded quarterly for 10 years, use the formula A = P(1 + r/n)^(nt). Plugging in the values, we get A = $5000(1 + 0.04/4)^(4*10), resulting in $7444.30 after 10 years.
Step-by-step explanation:
To calculate the future value of an investment with compound interest, you use the formula A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual 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, $5000 is invested at 4% interest compounded quarterly for 10 years. To solve this, we have:
- P = $5000
- r = 4% or 0.04
- n = 4 (since the interest is compounded quarterly)
- t = 10
Plugging these values into the formula, we get:
A = $5000(1 + 0.04/4)^(4*10)
Then calculate:
A = $5000(1 + 0.01)^(40)
A = $5000(1.01)^40
Now perform the exponentiation, and then multiply by the principal:
A = $5000 * (1.48886)
A = $7444.30
The amount after 10 years will be $7444.30.