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For a nine year period, Fiona deposited $600 each quarter into an account paying 5.2% annual interest compounded quarterly

(a) How much money was in the account at the end of 9 years? Show work.


(b) How much interest was earned during the 9 year period? Show work.


Fiona then made no more deposits or withdrawals, and the money in the account continued to
earn 5.2% annual interest compounded quarterly, for 5 more years.

(c) How much money was in the account after the 5 year period? Show work.


(d) How much interest was earned during the 5 year period?
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1 Answer

The formula for compound interest is A=P(1+r/n)nt
P=principle (Or amount that is put into the account)
In this case she is putting $600 in each quarter as well as the interest compounding quarterly.  so the formula for this one would look mre like this:
A=Pn1t1(1+r/n)n2t2
A=600n1t1(1+r/n)n2t2
r=rate (percentage changed to decimal form) In this case 5.2% = 0.052
A=600n1t1(1+0.052/n)n2t2
n1 &n2=how many times in a year the action is taken.  In this case both are done quarterly so 4 times per year n1=4 & n2=4
A=6004t1(1+0.052/4)4t2
t1 & t2=how many years
 
a)For this problem they give us t1 & t2=9years 
A=6004x9(1+0.052/4)4x9
A= $1.64e100
b)We have to subtract the principle (P-the money she deposited) to find out the interest earned from answer in a
$6.11e99
c) Now P=1.64e100 with no more deposits (n1 & t1=0), n2 still is still 4, and t2=5 so the formula looks like this
A=1.64e100(1+.052/4)4x5
A=$2.13e100
d) Again subtract the principle to find out the interest earned from the answer in c
$9.72e99
 
(I did not round off when calculating.)
 
I hope this helps!