Question

Please use PV, FV, R, PMT, N when answering.

1. Your best friend Frank just celebrated his 30th birthday and wants to start saving for his anticipated retirement. Frank plans to retire in 35 years and believes that he will have 20 good years of retirement and believes that if he can withdraw $90,000 at the end of each year, he can enjoy his retirement. Assume that a reasonable rate of interest for Frank for all scenarios presented below is 8% per year. This is an annual rate, review each individual question for more specifics on compounding periods per year. Because Frank is planning ahead, the first withdrawal will not take place until one year after he retires. he wants to make equal annual deposits into his account for his retirement fund. We are now back to Frank staring his retirement investments one year from now (35 years to retirement). Suppose Frank's employer will contribute $2,000 to the account each year as part of the company's profit sharing plan. In addition, assume that Frank has a trust fund that will pay out $25,000 to him when he is 50 (20 years from now). What amount must he deposit annually under these assumptions to be able to make the desired withdrawals at retirement? To find the amount of the annual deposit now, it is easier to break down the components of the problem. Doing so for each of the following to find your friend's annual deposit, we get:

D1) Value of employer's contribution at retirement :

D2) Value of trust fund at retirement :

D3) Remaining amount that Frank needs at retirement:

D4) (Final answer) Amount to save each year under these assumptions

Answer 1

D1) Value of employer's contribution at retirement can be calculated using the FV of an annuity formula as shown below:

Here n= time till retirement age or 35 years as the employer starts contributing from year 0

D2) Value of trust fund at retirement can be calculated by solving the below equation:

Here n= time till retirement age or 15 years as the trust fund contributes in year 20 so 35 - 20 = 15 years

D3) Remaining amount that Frank needs at retirement:

First of all let us calculate the PV of the total retirement spending amount required using the PV of an annuity formula:

Here n= total time of retirement or 20 years

Now we will subtract the amount contributed by the employer and the trust fund:

So 459695.43 is the amount that he needs to accumulate himself

D4) (Final answer) Amount to save each year under these assumptions

We need to solve for the PMT in the formula below:

Here n= time till retirement age or 35 years as Frank starts contributing from year 0

So he needs to save 2667.73 every year to meet his retirement goals.