When Frederick was born, his grandparents gave hime a gift of $2000, which was invested at an interest rate of 5% per year, compounded yearly. How much money will Frederick have when he collects the money at the age of 18? gGive your answer to the nearest hundreth of a dollar.
2000(1+.05)^18
It is invested compoundly
To calculate the amount of money Frederick will have when he collects it at the age of 18, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of money
P = the initial principal (the amount Frederick's grandparents gave him - $2000)
r = the annual interest rate (5% or 0.05)
n = the number of times interest is compounded per year (compounded yearly)
t = the number of years
Plugging in the values:
A = 2000(1 + 0.05/1)^(1*18)
A = 2000(1 + 0.05)^18
A = 2000(1.05)^18
Calculating this, we get:
A ≈ 2000(1.05)^18 ≈ 4035.72
Therefore, Frederick will have approximately $4035.72 when he collects the money at the age of 18.