child is now 3 years old - dad opens account with $10,000 it earns 4.5% annual intrest.
a) construct formula (A(t)=Ao(a)^t)
b) how much money will be in account when he is 10 years old
c) if dad wants account to grow to 100,000 when he is 18 then what should original amount to be
a) To construct the formula, we can use the formula for compound interest: A(t) = Ao * (1 + a)^t, where A(t) represents the amount in the account at time t, Ao represents the initial amount, a represents the annual interest rate (expressed as a decimal), and t represents the number of years.
In this case, Ao (the initial amount) is $10,000 and the annual interest rate (a) is 4.5% or 0.045 (expressed as a decimal). Thus, the formula becomes:
A(t) = $10,000 * (1 + 0.045)^t
b) To calculate how much money will be in the account when the child is 10 years old, we need to substitute t = 10 into the formula:
A(10) = $10,000 * (1 + 0.045)^10
Using a calculator or spreadsheet, we can evaluate this expression to find the answer.
c) If the dad wants the account to grow to $100,000 when the child is 18 years old, we need to determine the original amount (Ao) necessary to achieve this. Re-arranging the formula, we get:
Ao = A(t) / (1 + a)^t
Substituting the given values, we have:
Ao = $100,000 / (1 + 0.045)^18
Again, using a calculator or spreadsheet, we can evaluate this expression to find the original amount that should be deposited into the account.