To what amount will $ 4,800 invested for ten years at 9% compounded annually accumulate?
4800(1+.09)^10 = 11363.35
To calculate the accumulated amount, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the accumulated amount
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $4,800, the annual interest rate (r) is 9% (0.09 as a decimal), the number of times the interest is compounded per year (n) is 1 (compounded annually), and the number of years (t) is 10.
Substituting these values into the formula:
A = 4800(1 + 0.09/1)^(1*10)
A = 4800(1 + 0.09)^10
A = 4800(1.09)^10
Now, we can calculate the accumulated amount by using a calculator or by performing the exponential calculation:
A ≈ $11,146.29
Therefore, by investing $4,800 for ten years at a 9% annual interest rate compounded annually, the amount accumulated will be approximately $11,146.29.