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

Question

(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?

Answer 1

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=P^n1t1(1+r/n)^n2t2

A=600^n1t1(1+r/n)^n2t2

r=rate (percentage changed to decimal form) In this case 5.2% = 0.052

A=600^n1t1(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=600^4t1(1+0.052/4)^4t2

t1 & t2=how many years

 

a)For this problem they give us t1 & t2=9years 

A=600^4x9(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!