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Question 152528This question is from textbook
: Please help not really understanding this problem: The formula for calculating the amount of money returned for an initial deposit into a bank account or CD is given by A=P(1+r/n)^nt
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 $3000 for 9 years at a rate of 6%
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? Why?
d)If a bank compounds continuously, then the formula userdf is A=Pe^rt where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding. Round your answer to the hundredth's place.
e) How long will it take to double my money? At 6% interest rate and continuous compounding , what is the answer? Round your answer to the hundredth's place.
Thank you so much for your help in advance.
This question is from textbook
Answer by mducky2(62)   (Show Source):
You can put this solution on YOUR website! Part A: We can just plug in the numbers:
The principal amount (P) is 3000, since that is what was originally deposited.
The rate (r) is 0.06 because 6% means 6/100.
The number (n) that it is compounded is 1, since annually means only once a year.
The time (t) is 9 years.
The formula is much easier to deal with when we first plug in n=1, so let's start with that:
This is also the general formula for the return on any deposit compounded annually. Now we can plug in the specific numbers:
The return is $5068.44.
Part B: We can just plug in the numbers. P, r, and t are the same, but now n changes from 1 to 4:
This is also the general formula for the return on any deposit compounded quarterly. Now let's plug in the numbers:
The return is $5127.42
Part C: Compounding quarterly yields more interest. This is because when we do it once a year, it only multiplies the whole thing once by 1.06. When we do it four times a year, it multiplies it by 1.015^4, which is 1.06136355, which is actually more than 1.06.
Part D: Now we will use a different formula entirely.
We can still plug in the same numbers for P, r, and t.
The return is $5148.02
Part E: In order to find out how much it will take to double the money, we start with the equation:
The variables P and r will be the same, but we no longer know how much time it will take.
It looks like we need to use logarithms to solve this problem. The natural log of 2 will equal 0.06*t:
It should take 11.55 years for the deposit to double.
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