(a)
Interest rate is 15% comoounded quarterly.
So effective Interest rate is per quarter is 0.15/4 = 0.0375
Deposit is made Yearly. so effective interest rate per annum formula
Effective interest rate =((1+ quarterly rate)^no of quarter)
((1+ 0.0375)^4)-1 = 0.158650415
So, annual interest rate= 0.1587 or 15.87%
(b)
Quarterly Annuity required from 65th birthday to 75 th birthday. =$
10000
75th birthday is included and first withdrawl is made at time of
last deposit. So it is Annuity due from 65th to 75th birthday.
Number of quarters shall be (1+(10*4))= 41 quarters (as at 65th
birthday Amount is withdrawn)
Quarterly Interest rate = 0.0375
We need to Calculate present Value of annuity to Calculate Amount
that must have at the time of 17th birthday for Annuity withdrawl
of $4000
Present Value of annuity due formula = Annuity
*(1+i)*(1-(1/(1+i)^n))/i
10000*(1+0.0375)*(1-(1/((1+0.0375)^41)))/0.0375
215,509.90
We must have accumulated $215509.90 at the time of 65th birthday.
To Calculate present worth at (t=0) no. of periods =
(65-40)= 25 years.
Future value is $215509.90 in respect to today time.
Present Value = Future value/(1+i)^n
215509.90/(1+0.158650415)^25
=$ 5428.210582
So, present worth is $5428.
(c)
To Calculate annual deposit for future value of $215509.90, Future
value of Annuity formula will become applicable.
Deposit is made from 40th birthday itself to 65th birthday. So
Total periods (n) = 26
Future value of annuity formula = P *{ (1+r)^n - 1 } / r
215509.90 = P*(((1+0.158650415)^26)-1)/0.158650415
215509.90/ 283.6459214 =P
P = 759.7849419
So, We need to contribute $760 annually.
Problem D. Given the following problem, answer questions 32 to 34. J. Doe is turning 40...
Problem G Given the following problem, answer question 36 to 38 A. Adams is turning 40 years old today and plans to retire on his 65 birthday. He starts making annual doposits (starting on the day of his 40h birthday) into an account that pays 15% compounded quarterly. He plans to withdraw $10,000 quarterly from the account starting on his 65h birthday until his 75th birthday (inclusive). Note that the last deposit is made at the same time as the...