Question

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 first withdrawal. 36. What is the effective interest rate for the deposits? a) 3.75% c) 15.87% b) 15% d) 16.80% 37. What is the present worth (now) of the withdrawals? a) $4,895 c) $ 5,176 b) $ 5,015 d) $ 5,428 38. What is the amount of the deposits? b) $ 812 d)$ 907 a) $ 760 c) $ 862

Answer 1

Ans 36)

Effective interest rate= (1+r/4)^4=(1+(15%/4))^4-1=15.865%

Hence option A is correct

Ans 37)

Total Present worth of withdrawals = PW of $10000 withdrawal made on 65th birthday +PW of $10000 withdrawal made on 66th birthday +PW of $10000 withdrawal made on 67th birthday +...+PW of $10000 withdrawal made on 75th birthday

=10000/(1.0375)^100+10000/(1.0375)^101+10000/(1.0375)^102+...+10000/(1.0375)^140

=10000/(1.0375)^100(1+(1/1.0375)+...+(1/1.0375)^40)

=(10000/(1.0375^100))*(1-(1/1.0375)^41)/(1-(1/1.0375))

=5428.21

Hence Option D is correct

Ans 38)

We have PW from Ans 37)

Amount of Deposit =Annual Worth =PW/(P?A,15.86%,25)=5428.21/6.1679=880.3

Hence the closest answer is $862

Option C is correct