SOLUTION: I NEED HELP WITH THIS PROBLEM TUTORS. THANKS THE FORMULA FOR CALCULATING THE AMOUNT OF MONEY RETURNED FOR AN INITIAL DEPOSIT INTO A BANK ACCOUNT OR CD )CERTIFICATE OF DEPOSIT) IS

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Question 116300: I NEED HELP WITH THIS PROBLEM TUTORS. THANKS
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=P[1+R/N]
A=AMOUNT OF THE RETURN
P=PRINCIPAL AMOUNT INITIALLY DEPOSITED
r=the annual interest rate (expressed as a decimal)
n=the number of compound periods in one year.
t= is the number of years.
CARRY ALL CALUCULATIONS TO SIX DECIMALS ON EACH INTERMEDIATE STEP, THEN ROUND THE FINAL ANSWER TO THE NEAREST CENT.
sUPPOSE YOU DEPOSIT $4,000 FOR 8 YEARS AT A RATE OF 7%
A) CALCULATE THE RETURN (A) IF THE BANK COMPOUNDS ANNUALLY (N=1). ROUND YOUR ANSWER TO THE HUNDRETH'S PLACE.
ANSWER:
SHOW YOUR WORK:
B) CALCULATE THE RETURN (A) IF THE BANK COMPOUNDS MONTHLY (N=12).ROUND YOU ANSWER TO THE NEAREST HUNDRETH'S PLACE.
ANSWER:
SHOW YOUR WORK:
C) DOES COMPOUNDING ANNUALLY OR MONTHLY YIELD MORE INTEREST? EXPLAIN WHY?
ANSWER:
SHOW YOUR WORK:
D) IF A BANK COMPOUNDS CONTINUOUSLY, THEN THE FORMULA USED IS A=Pe^rt
were e is a constant and equals approximatly 2.7183. Calculate A with continuous compounding. Round your answer to the hundreth's place.
answer:
show your work:
E) A COMMONLY ASKED QUESTION IS,"HOW LONG WILL IT TAKE TO DOUBLE MY MONEY?" AT 7% INTEREST RATE AND CONTINUOUS COMPOUNDING, WHAT IS THE ANSWER? ROUND YOUR ANSWER TO THE HUNDRETH'S PLACE.
ANSWER:
SHOW YOUR WORK.
NEED HELP ASAP. THANK YOU VERY MUCH TUTOR!!
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
A+=+P+%281+%2B+r%2Fn%29%5E%28nt%29
A is the amount of returned
P is the principal amount deposited
r is the annual interest rate (expressed as a decimal)
n is the compound period
t is the number of years
a)
n+=+1
P+=++4000+$
r = 7%
t+=+8

A+=+P+%281+%2B+r%2Fn%29%5E%28nt%29

A+=+4000+%281+%2B+.07%2F1%29%5E%281%2A8%29

A+=++4000+%281+%2B+.07%29%5E8

A+=+4000+%281.07%29%5E8

A+=++4000+%281.72%29

A+=+%24+4000+%281.72%29

A+=+%24+6880…….$

b)
given:
n+=+12
P+=+4000+
r = .07
t+=+8
A+=+P+%281+%2B+r%2Fn%29%5E%28nt%29

A+=++4000+%281+%2B+.07%2F12%29%5E%2812%2A8%29

A+=+4000+%281+%2B+.0058%29%5E96

A+=+4000+%281.+0058%29%5E96

A+=+4000+%281.74%29

A+=+4000+%281.74%29

A+=++6960…….$

c)
compounding monthly yield more interest; the more frequently an account pays interest, the faster you can start earning interest on interest
Compounded annually:
A+=+P+%281+%2B+r%2Fn%29%5E%28nt%29

A+=+4000+%281+%2B+.07%2F1%29%5E1

A+=+4000+%281.07%29%5E1

A+=+4000+%281.07%29

A+=+4280 …….$

Compounded monthly:
A+=+P+%281+%2B+r%2Fn%29%5E%28nt%29

A+=+4000+%281+%2B+.07%2F12%29%5E12

A+=+4000+%281.07%29%5E12

A+=+4000+%282.52%29

A+=+10080 …….$

d)

let
P+=+4000+

r = .07

t+=+8
answer:
A=Pe%5E%28rt%29

A=4000%282.7183%29%5E%28.07%2A8%29

A=4000%282.7183%29%5E%28+0.56%29

A=4000%281.75%29

A=+7000… …….$

e)

let
P+=++4000+
if A=+7000… …….$.....double is 2A=+14000…

r = .07

t+=+t
answer:

A=Pe%5E%28rt%29

e%5E%28rt%29+=+A%2FP

%28e%29%5E%28.07t%29+=+14000%2F4000

%28e%29%5E%28.07t%29+=+14%2F4

%28e%29%5E%28.07t%29+=+3.5

ln%28e%5E.07t%29+=+ln%283.5%29

.07t+=+1.253

t+=+1.253%2F.07

t+=+17.90..years