Question

John made equal monthly (end-of-the month) deposits into an account for 10 years (total of 120 deposits). He then made equal monthly (end-of month) withdrawals (the first withdrawal occurs one month after the last deposit) of $1,000 for the next 12 years (total of 144 withdrawals), reducing the balance to zero. The account pays 8.4 percent per year compounded monthly. What was the monthly deposit?

Answer 1

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

Using Financial calculator:

N= 144

I/Y = 8.4/12 = 0.7

PMT = -1000

CPT Press PV = 90,538.29

(Amount needed at t=10)

N= 120

I/Y= 0.7

FV = -90,538.29

CPT Press PMT = 483.94

The amount you need to contribute each month is = $483.94

(ANSWER)

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 = 1000× [1-(1+0.007)^144-]/0.007

PV = 90,538.29

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.

90,538.29= C× {[(1+0.007)^120]-1}/0.007

C= $483.94

The amount you need to contribute each month is =$483.94 (ANSWER)