Question

"You plan on saving money for retirement in 30 years (t=30) at which time, you wish to have saved $1,000,000. In order to do this, you plan on depositing $10,000 into the bank for 10 years starting next year (last $10,000 deposit at t=10). And then deposit $x every year after that until your retirement day (last deposit of $x at t=30). If the interest rate is 6% per annum, what is the $x you must deposit?"

Answer 1

X= $15,692.9393

Step-by-step explanation:

Giving the following information:

Number of years= 30

Final value= 1,000,000

First, deposit $10000 for ten years (last deposit at t=10).

After ten years, you deposit X for 20 years until t=30.

i= 6%

First, we need to calculate the final value in t=10. We are going to use the following formula:

FV= {A*[(1+i)^t-1]}/i

FV= {10000*[(1.06^10)-1]}/0.06= $131807.9494

We can calculate the amount of money to input every year. We need to isolate A:

A= (FV*i)/[(1+i)^n-1]

First, we need to calculate the final value of the $131807.9494

FV= PV*[(1+i)^n]

FV= 131807.9494*1.06)^20= 422725.95

We need (1000000-4227725.95) $577274.05 to reache $1000000

A= (FV*i)/[(1+i)^n-1]

A= (577274.05*0.06)/[(1.06^20)-1]= 15692.9393

X= $15,692.9393