Question 33423: Maybe it is because the problem is so long it is overwhelming or maybe it is just going right over my head, but can someone please help me with this, it would be greatly appreciated......
The formula for calculating the amount of money returned for an initial deposit money into a bank account or CD (Certificate of Deposit) is given by A = P (1 + r/n)^nt
A is the amount of returned.
P is the principal amount initially deposited.
r is the annual interest rate (expressed as a decimal).
n is the compound period.
t is the number of years.
Suppose you deposit $10,000 for 2 years at a rate of 10%.
a) Calculate the return (A) if the bank compounds annually (n = 1).
b) Calculate the return (A) if the bank compounds quarterly (n = 4).
c) Calculate the return (A) if the bank compounds monthly (n = 12).
d) Calculate the return (A) if the bank compounds daily (n = 365).
e) What observation can you make about the increase in your return as your compounding increases more frequently?
f) If a bank compounds continuous, then the formula takes a simpler, that is
A = Pe^rt
where e is a constant and equals approximately 2.7183.
Calculate A with continuous compounding.
g) Now suppose, instead of knowing t, we know that the bank returned to us $15,000 with the bank compounding continuously. Using logarithms, find how long we left the money in the bank (find t).
h) A commonly asked question is, “How long will it take to double my money?” At 10% interest rate and continuous compounding, what is the answer?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! You're right; it's a long one. I'll pick out some pieces
to give you an example of how to work on these; the rest
I'll leave to you.
c) A=10,000(1+(0.10/12)^(0.10*2)
A=10,000(1+0.0083)^(0.2)
A=10,000(1.008333)^0.2)
A= $10797.75
f) A=Pe^(rt)
A=10000e^(0.10(2))
A=10000e^0.2
A=$12214.03
h)20,000=10000e^(0.10t)
2=e^0.10t
ln2 =0.010t
t=(ln2)/(0.10)
t= 6.93 yrs
Hope this helps.
Cheers,
Stan H.
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