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.

Is this answer right? 4183.24