Question

You have just turned 22 years​ old, received your​ bachelor's degree, and accepted your first job. Now you must decide how much money to put into your retirement plan. The plan works as​ follows: Every dollar in the plan earns 6.7 % per year. You cannot make withdrawals until you retire on your 65th birthday. After​ that, you can make withdrawals as you see fit. You decide that you will plan to live to 100 and work until you turn 65. You estimate that to live comfortably in​ retirement, you will need $ 110 comma 000 per​ year, starting at the end of the first year of retirement and ending on your 100th birthday. You will contribute the same amount to the plan at the end of every year that you work. How much do you need to contribute each year to fund your​ retirement?

how can you solve this manually and on a financial calculator?

Answer 1

ANSWER DOWN BELOW. FEEL FREE TO ASK ANY DOUBTS. THUMBS UP PLEASE.

Using Financial calculator:

N= 100-65
I/Y = 6.7
PMT = -110,000
CPT Press PV = 1472137.40
(Amount needed at age 65)

N= 65-22
I/Y= 6.7
FV = 1472137.40
CPT Press PMT = 6464.3
Amount you need to contribute each year is = 6464.3

Normal method:

Formula: The present value of an ordinary annuity (PV)

PV = C× [1-(1+r)^-n]/r

PV = Present value (The cummulative amount available at Present)
C= Periodic cash flow.
r =effective interest rate for the period.
n = number of periods.

PV = 110000× [1-(1+0.067)^-35]/0.067
PV = 1472137.40

Formula: The Future Value of an ordinary annuity (FV)

FV= C× {[(1+r)^n]-1}/r

FV = Future value (The cummulative amount available in Future)
C= Periodic cash out flow.
r =effective interest rate for the period.
n = number of periods.

1472137.40 = C× {[(1+0.067)^43]-1}/0.067
C= 6464.3

The amount you need to contribute each year is = 6464.3