Question 125490: These questions have really got me stumped! I dont understand some problems sometimes, and these are a few of them, they all use the following formula to solve it. Thank you so much, Have a blessed day!!
The formula for calculating the amount of money returned for an initial deposit into a bank account or CD (certificate of deposit) is given by
A is the amount of the return.
P is the principal amount initially deposited.
r is the annual interest rate (expressed as a decimal).
n is the number of compound periods in one year.
t is the number of years.
Carry all calculations to six decimals on each intermediate step, then round the final answer to the nearest cent.
Suppose you deposit $2,000 for 5 years at a rate of 8%.
a) Calculate the return (A) if the bank compounds annually (n = 1). Round your answer to the hundredth's place.
b) Calculate the return (A) if the bank compounds quarterly (n = 4). Round your answer to the hundredth's place.
c) Does compounding annually or quarterly yield more interest? Explain why
d) If a bank compounds continuously, then the formula used is
where e is a constant and equals approximately 2.7183.
Calculate A with continuous compounding. Round your answer to the hundredth's place.
e) A commonly asked question is, “How long will it take to double my money?” At 8% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth's place.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Parts a and b of your problem are just plugging in numbers and doing the arithmetic. For a, put 1 in for n, 5 in for t, and convert 8% to a decimal, namely 0.08, and put that in for r.
For b, same thing, except you put in 4 for n.
You can punch numbers on a calculator as well as I can so I'll leave that part to you.
Part c asks about the difference between compounding annually or quarterly. Let's look at an example. Say you had $1000 in the bank at 4% for one year.
At the end of a year of annual compounding, you would have $1040, or a $40 yield. But if it was quarterly compounding, at the end of the first quarter, they would pay 1% or $10, so you would have $1010. At the end of the second quarter you would receive another 1% interest, but paid against the new $1010 balance, so you would get an interest payment of $10.10 making your balance $1020.10. The next quarter your interest payment would be $10.201 and the balance would be $1030.301, and the last quarter, you would get $10.303, for a balance of $1040.602, or $.60 better than you did compounding annually. In general, the more frequently you compound, the greater the yield for a given rate of annual interest -- that's because you are being paid interest on interest already earned.
Part d. You left off the formula, but it is  . Just remember the word PERT.  . If you use the calculator built in to Windows, turn on the scientific mode, click the INV checkbox, click the 1 key, click the ln function key, (you should have the value for e - 2.7183...), multiply, 0.2,multiply,2000. You should get roughly $2442.81
Part e.
Start with
We want to solve for t when A = 2P, so
 , but  , so
and finally 
For a rate of 8%, 
On the Windows calculator, press 2, press the ln (ln means  )function key, divide, .08, equals roughly 8.66.
There is a quick way to approximate the time it takes for money to double. You divide 72 by the interest rate as a whole number. In this case 72/8 = 9 -- way close enough if you need to do the calculation quickly in your head.
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