Question

On the advice of his C.P.A., a 50 year-old sole-proprietor begins an I.R.A. to save for his retirement.  He makes a series of 15 equal deposits (the first such deposit is made in one year and the last when he is 65).  When he turns 66, the businessman wants to withdraw $35,000 per year for 20 years.  If money grows at 4.3 % (effective rate) during the accumulation period and at 3.3% per annum thereafter, how much money does he need to deposit into his retirement fund each year?

Ira Saver has been depositing $12,000 into a retirement plan at the end of each of the last 15 years.  His deposits have grown at 5% effective for the first 9 years, at 4 % for the next 4 years and at 3% thereafter.  What is the accumulated amount in his retirement plan just after having made his last deposit?

To settle a debt obligation, a person agrees to pay $1,200 at the end of each semi-annual period – the first such payment to be made in 6 months with a total of 23 full payments and a final 24th payment of $950.  If the debt is at j2 = .036, what is the present value of the obligation?

A woman dies, leaving her only surviving daughter an estate of $50,000.  The money is invested at j (4) = 8%.  How many quarterly payments of $1500 will the daughter receive?  What would be the amount of any final payment, were it to be paid 3 months after the last full $1500 installment?

Find the present value of a perpetuity paying $55 per month if j (12) = 6%

Answer 1

the amount required to be deposited into his retirement account every year =     $ 24,739.25

Steps :

first lets find out the funds required at the end of retirment period to provide for 35000p.a for 20 years post retirement

This is the Present value of the Future annuity streams- at the time of retirement

Annual Payment of annuity           Pmt = 35,000

   rate of interst   post retirment        r     = 3.3% or   0.033

number of years in which pmt made n    = 20 years

we know,

                   PV of annuity Streams           

       

                                                             

                                                             =   $ 506,557.70

so our target of funds to be held at retirement of 65 years = 506,557

to acheive this target- an annuity investment is made for 15 years at 4.3% p.a. we need to find the amount of annuity investment made each year.

FV of Retirement funds    = 506557.70

Number of years of investment N   = 15 years

Rate at which invested             R = 4.3% or 0.043

to arrive at the annuity amount,   we need the PV of the retirement funds

PV of retirement funds =   FV of retirement funds/ ( 1+ R)^_N

                                               = 506557.70     /   ( 1+0.043)¹⁵

                                                 ⁼   269,379.35

now lets find out the annuity investment to be made for 15 years

           

                            

                             =     $ 24,739.25

the amount required to be deposited into his retirement account every year for 15 years is =     $ 24,739.25