Question

A) You plan to deposit $2,000 per year for 6 years into a money market account with an annual return of 3%. You plan to make your first deposit one year from today.

- What amount will be in your account at the end of 6 years?
Round your answer to the nearest cent. Do not round intermediate
calculations.

$ - Assume that your deposits will begin today. What amount will be
in your account after 6 years? Round your answer to the nearest
cent. Do not round intermediate calculations.

$

B) You and your wife are making plans for retirement. You plan on living 25 years after you retire and would like to have $100,000 annually on which to live. Your first withdrawal will be made one year after you retire and you anticipate that your retirement account will earn 10% annually.

- What amount do you need in your retirement account the day you
retire? Round your answer to the nearest cent. Do not round
intermediate calculations.

$ - Assume that your first withdrawal will be made the day you
retire. Under this assumption, what amount do you now need in your
retirement account the day you retire? Round your answer to the
nearest cent. Do not round intermediate calculations.

$

Answer #1

A).

Given that the deposits will be $2000 per year for 6 years, with annual return of 3%.

a. As the first payment is one year from now, this is an ordinary Annuity. We need to find the future value of annuity using the following formula, P*(((1+r)^n)-1)/r.

On substituting , we get 2000*(((1+3%)^6)-1)/3%

= 2000*(((1.03)^6)-1)/0.03

= 2000*(0.1941)/0.03

= 388.1/0.03

= 12936.82

b. If the first payment begin today, it will be annuity due. The formula for future value of annuity due changes slightly as (P*(((1+r)^n)-1)/r)*(1+r)

On substituting, we get

(2000*(((1.03)^6)-1)/0.03)*(1.03)

= 12936.82*1.03

= 13324.92

B).

Given that withdrawals will be $100000 for 25 years, at 10% interest.

a. As the first withdrawal is made one year from the date of retirement, this is ordinary annuity. We need to find the present value of annuity using the formula:

P*((1-(1+r)^-n)/r)

On substituting, we get

100000*((1-(1.1)^-25)/0.1)

= 100000*(0.907704/0.1)

= 100000*9.07704

= 907704.00

b. If the first withdrawal is done today, it will be annuity due. The formula for present value of annuity due changes slightly as (1+r)*(P*((1-(1+r)^-n)/r)

On substituting, we get 1.1*(100000*(1-(1.1^-25))/0.1

= 1.1*907704

= 998474.40

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