Question

Please answer with steps for BA II finc. calculator (not excel steps)

a. You anticipate that you will need $1,500,000 when you retire 30 years from now. You just join a new firm and your first annual salary is $100,000 to be received one year from today. You also received one time signing bonus of $50,000 today. You decided that you will put all you signing bonus into your account plus you will contribute $X every year starting next year for the next 29 years. In other words, after your initial deposit of $50,000, your first payment will be made on year 1 and last payment will be on year 29. How much is $X if you want to have $1,500,000 in Year 30. Assume that interest rate is 8%, compounded annual during this duration.

1. $1,388,888.89
2. $1,288.,888.89
3. $106,159.09
4. $98,150.35
5. $8,878.15

b. You are saving for your child's education since you did not participate in the Texas Tomorrow Fund. Your child is five-year-old today. Starting next quarter, you will deposit $300 every quarter until you child turns 17. Your last payment will be on his 17th year.You can to withdraw $X every year starting his 18th birthday for 4 years (first payment on his 18th birthday). Assuming you have investing your money in an account is provides 12% return, and the interest is compounded daily (365 days), what is X?

1. $13,826.63
2. $11,998.78
3. $10,608.75
4. $8,982.45
5. $5,782.88

Answer 1

1) Annuity means a specific amount being paid in equal frequency to make up a specific future value.

Future value of annuity is given by formula = P {(1+R)^N-1}/R

Where P is the annuity amount contributed each year which is X in the givven question. In the BA II Fin cal it is PMT

R= rate of return = 8%, in BA II Fin cal, I/Y=8

N= no of years =29, in BA II Fin cal, N=29

In the question $50000 is invested at day 1 ie, it shall be invested for 30 years. We will put PV

So the equation becomes 1,500,000= 50000(1.08)30 + X { (1.08)^29-1}/.08

In the Fin Cal we shall first calculate the FV of the 50000 invested on Day 1.

I/Y=8, N=30 , PV=50000 , CPT- FV = $503,133

We shall deduct this from the retirement value ie money to be deposited every year to make a net of =1500000-503133

=996,867

AMOUNT X can be found out by BA II Fin cal as per the below

I/Y=8, N=29, FV =996867, CPT- PMT =$9,588

the amount to be invested every year = $ 9,588

b)   The amount invested is quarterly and frequency of the amount withdrawn is annual although the rate of return is compunded daily.

We need to calculate the rate of return compunded quarterly = (1+ .12/365) ^365/4

=   3.045% compunded quarterly

Rate of return compounded annually = (1 + .03045)^ 4

=12.75 % compounded annually

First we need to calculate the FV that will accumulate at 17 years of age

PMT=300, N= 12*4 = 48 , I/Y= 3.045 , CPT-> FV =$ 31,722 ,

The $300 will make up to $ 31,722 at a interest rate of 3.045 compounded quarterly for a period of 12 years.

The amount to be withdrawn every year shall be calculated using BA II Fin cal is given below.

PV=31722, I/Y=12.75, N=4, CPT->PMT = $10609

The amount withdrawn shall be $ 10,609.