Answer to Question #171091 in Financial Math for saleemaslam

Question

 

1. Amy made semiannual deposits of $3,100 at the beginning of every every six months into a fund earning 6.8% compounded semiannually for nine years. No further deposits were made.

   a. How much will be in the account 15 years after the first deposit? _____________    

   b. How much in total was deposited? ______________

c. How much interest will Amy earn? _____________

 

 

2. What is the principal invested at 4.75% compounded semiannually from which monthly withdrawals of $240 can be made at the beginning of each month for 15 years? _________________

 

 Need it in 7 hours

 

 

 

 

 

 

Answer 1

1.a) In the account after 9 years:

$FV_9=(R(1+i)^n-1)/i$

$FV_9=(3100\cdot1.068^{9\cdot2}-1)/0.068=\$148967.82$

In the account after 9 years:

$FV_{15}=FV_9(1+i)^n$

$FV_{15}=148967.82\cdot1.068^{6\cdot2}=\$328055.63$

b) It was deposited:

$P=3100\cdot9\cdot2=\$55800$

c) Amy will earn:

$FV_{15}-P=328055.63-55800=\$272255.63$

2.

$P_0=d(1-(1+i)^{-n})/i$

$P_0=240(1-(1+0.0475/6)^{-15\cdot12})/0.0475/6=\$22983.56$