Question

If you desire to have $60200 for a down payment for a house in 8 years, what amount would you need to deposit today? Assume that your money will earn 6 percent. Pete Morton is planning to go to graduate school in a program of study that will take 3 years. Pete wants to have $18100 available each year for various school and living expenses. If he earns 4 percent on his money, how much must be deposit at the start of his studies to be able to withdraw $18100 a year for 3 years? Carla Lopez deposits $6090 a year into her retirement account. If these funds have an average earning of 9 percent over the 18 years until her retirement, what will be the value of her retirement account?

Answer 1

1. Answer : You would need to deposit $ 37,770 today.

Future value = $ 60,200.

Principal x ( 1.06 ) ⁸ = $ 60,200

or Principal = $ 60,200 / 1.59385 = $ 37,770

2. Answer: Pete must deposit $ 50,229 at the start of his studies.

Present value of annuity of $ 1 at 4 % for 3 years = [ { 1 - ( 1 / 1.04) ³ } / 0.04 ] = 2.77509

Present value of $ 18,100 at 4 % for 3 years = $ 18,100 x 2.77509 = $ 50,229.13

3. Value of Carla's retirement account : $ 251,525

Future value of an annuity of $ 1 at 9 % for 18 years = [ { ( 1.09 ) ¹⁸ - 1 } / 0.09 ] = 41.30134

Therefore, future value of annuity of $ 6,090 at 9 % for 18 years = $ 6,090 x 41.30134 = $ 251,525.16