Michelle invests some money in a savings account. It pays 4% compounded annually.
- Thread starter FireBall
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You don't need an amount. You are given that A = 2P, so use the regular compound-interest formula, and plug "2P" in for "A".
lev888
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You don't need the initial amount for the same reason you don't need it for this problem:
Mary gave Michelle $2 and $3. Michelle says "I now have $6 more". Michelle is wrong, explain why.
Steven G
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The interest is compounded! Mary is suggesting that since 4%*25 = 100%, she will have doubled her money after 25 years. This is true only if she doesn't get any interest on her earned interest.
Now suppose that if you put $100 into one account and $50 into another account both paying the same interest rate. If the $50 doubles sooner than the $100, then you should NOT deposit $100 into this saving account. Rather you should make two savings account of $50 each. In fact, you should make 4 accounts of $25 each. Actually, it would be best if you make 8 accounts of $12.50 each.....
If the $100 doubles before the $50 does, then you should NEVER have more than one savings account!
Have you ever heard anyone say this to you? I suspect not, as it is not true. Any amount of money will double on the same day given any interest rate.
Recall that the formula you are using is A(t) = P(1+r/n)nt, where P is the amount you put into this savings account. Your money will double when you have 2P in this account. So solving for t for 2P= P(1+r/n)nt, the first thing you can do is divide by P which results in 2 = (1+r/n)nt showing that the value that you invested, namely P, doesn't even matter. That is no matter what P equals, your money will double (or triple or increase by 28%,...) on the same day ! What this really means is that each dollar that you invests grows at the same rate.
Now suppose that if you put $100 into one account and $50 into another account both paying the same interest rate. If the $50 doubles sooner than the $100, then you should NOT deposit $100 into this saving account. Rather you should make two savings account of $50 each. In fact, you should make 4 accounts of $25 each. Actually, it would be best if you make 8 accounts of $12.50 each.....
If the $100 doubles before the $50 does, then you should NEVER have more than one savings account!
Have you ever heard anyone say this to you? I suspect not, as it is not true. Any amount of money will double on the same day given any interest rate.
Recall that the formula you are using is A(t) = P(1+r/n)nt, where P is the amount you put into this savings account. Your money will double when you have 2P in this account. So solving for t for 2P= P(1+r/n)nt, the first thing you can do is divide by P which results in 2 = (1+r/n)nt showing that the value that you invested, namely P, doesn't even matter. That is no matter what P equals, your money will double (or triple or increase by 28%,...) on the same day ! What this really means is that each dollar that you invests grows at the same rate.
Are you familiar with "rule of 72" ?
That will give a close approximation of the answer for 6(b).