SOLUTION: Starting with the first, on each of Gideon's birthdays, Dr. Prince deposits $1000 into an account earning 5.7% interest compounded annually.
What is the total amount in the acco
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What is the total amount in the acco
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Question 1121031: Starting with the first, on each of Gideon's birthdays, Dr. Prince deposits $1000 into an account earning 5.7% interest compounded annually.
What is the total amount in the account after the deposit made on Gideon's eighteenth birthday? $__________
How much should Dr. Prince have deposited each year if he had wanted the account to be worth $138000 on Gideon's eighteenth birthday? $__________ Found 2 solutions by Alex.33, ikleyn:Answer by Alex.33(110) (Show Source):
You can put this solution on YOUR website! Given that every year he deposited $1000 and the annual interest rate is 5.7%(compounded)
assume the amount at his nth birthday to be a[n].
also assume the amount of money deposited each year to be a[1]=x, a[n]=(a[n-1]+x)*1.057=1.057a[n-1]+1.057x.
Therefore,
a[n]=1.057^(n-1)*a[1]+x*(1.057^(n-1)+1.057^(n-2)+...+1.057)
=1.057^(n-1)*x+(1.057*(1.057^(n-1)-1)/(1.057-1))*x//sum of the Geometric Sequence
=x*((1.057^(n-1))*(1+1.057/0.057)-1.057/0.057)
=x*((1.057^(n-1))*(1114/57)-(1057/57))
To this step, we can know the amount in the account at the nth birthday for any given value of x deposited annually.
1. n=18, x=1000. I get a[18]=31607.77804.(approximate)
2. n=18, a[n]=138000. I get x=4366.013954. (approximate)
(there's something wrong with the fomula display at the time I was editing. My Apology.)
