I personally think the solution of this question is wrong somewhere does anyone
ID: 1170459 • Letter: I
Question
I personally think the solution of this question is wrong somewhere does anyone can help to point it out and explain to me
Question 2 Since June 30, 2010 Smith has been making deposits of $100 each into a bank account on the last day of each month. For all of 2010 and 2011 Smith's account earned nominal interest compounded monthly at an annual rate of 9%. For the first 9 months of 2012 the account eamed0.105, and since then the account has been earning i0.12. Find the balance in the account on February 1, 2013 0123 (12)Explanation / Answer
Accumulated balance at end of year 2011
FV of annuity = A[(1+r)^n-1/r]
=100[(1+0.0075)^19-1/ 0.0075]
=100[(1.0075)^19-1/0.0075]
=100[1.15254-1/0.0075]
=100*20.33868
=2033.868$
Now calculating accumulated balance at end of 8 months in year 2012
Monthly rate = 10.5/12 = 0.875%
FV of annuity = A[(1+r)^n-1/r]
=100[(1+0.00875)^8-1/ 0.00875]
=100[(1.00875)^8-1/0.00875]
=100[1.07218-1/0.00875]
=100*8.2493
=824.93$
Balance of accumulated balace of 2011
FV = PV(1+r)^n
=2033.868(1.00875)^8
=2033.868(1.07218)
=2180.676
Total accumualated balance as end of 8th month of year 2012
=2180.676+824.933
=3005.933$
Calculation showing account balance as on Feb 1, 2013
Rate = 12/12 = 1%
FV of annuity = A[(1+r)^n-1/r]
=100[(1+0.001)^5-1/ 0.001]
=100[(1.001)^5-1/0.001]
=100[1.00501-1/0.001]
=100*5.01001
=501.001$
Balance of accumulated balace as at end of 8th month of 2012
FV = PV(1+r)^n
=3005.6095(1.001)^5
=3005.6095(1.00501)
=3020.667$
Total accumualated balance as on 1st feb of year 2013
=3020.667+501.001
=3521.668$