Please provide formulas if possible.

In order to answer any of these questions, first we need to know how much your friend will need when she is ready to retire. Since this amount will be the same for each of the parts of the problem, we will solve for this amount now, which will be: Amount needed at retirement: a. The amount your friend must save each year to fund her retirement is: Amount to save each year: b. The lump sum your friend must deposit today to fund her retirement is: Lump sum deposited today: 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: Value of employer's contribution at retirement: Value of trust fund at retirement: Amount to save each year now: This is a classic retirement problem. A friend is celebrating her birthday and wants to start saving for her anticipated retirement. She has the following years to retirement and retirement spending goals: 30 Years until retirement: Amount to withdraw each year: Years to withdraw in retirement: Interest rate: 90,000 20 8% Because your friend is planning ahead, the first withdrawal will not take place until one year after she retires. She wants to make equal annual deposits into her account for her retirement fund. If she starts making these deposits in one year and makes her last deposit on the day she retires, what amount must she deposit annually to be able to make the desired withdrawals at retirement? Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments, she has decided to make one lump sum deposit today to cover her retirement needs. What amount does she have to deposit today? Suppose your friend's employer will contribute to the account each year as part of the company's profit sharing plan. In addition, your friend expects a distribution from a family trust several years from now. What amount must she deposit annually now to be able to make the desired withdrawals at retirement? $ 1,500 Employer's annual contribution: Years until trust fund distribution: Amount of trust fund distribution: 20 $ 25,000