Question

Suppose an individual makes an initial investment of $1,400 in an account that earns 7.8%, compounded monthly, and makes additional contributions of $100 at the end of each month for a period of 12 years. After these 12 years, this individual wants to make withdrawals at the end of each month for the next 5 years (so that the account balance will be reduced to $0). (Round your answers to the nearest cent.)

(a) How much is in the account after the last deposit is made?
$  

(b) How much was deposited?
$  

(c) What is the amount of each withdrawal?
$  

(d) What is the total amount withdrawn?

Answer 1

Future value of initial investment $1,400 in an account that earns 7.8%, compounded monthly

FV (Initial investment) = 1400*(1+0.078/12)^144 = $3558.87

For finding future value (after 12 years) of the monthly contribution we use a financial calculator,

PV = 0

PMT = 100

N = 144 (12 years*12 months = 144 periods)

I/Y = 7.8/12 (Interest per period)

cpt FV, we get

FV = -23723.85

Hence, the value of monthly deposits after 12 years = 23723.85

Total value of deposits after 12 years = $(23723.85+3558.87) = $27282.72

Now, this total value of deposits is withdrawn monthly over a period of 5 years

We use a financial calculator to find PMT

PV = -27282.72

FV = 0

I/Y = 7.8/12 (Interest per period)

N = 60 (5 years*12 months = 60 monthly payments)

cpt PMT, we get

PMT = 550.59

Hence, amount of each withdrawal for 5 years = $550.59

How much is in the account after the last deposit is made? => $27282.72

How much was deposited? = 1400 + 144*100 = $15800

What is the amount of each withdrawal? => $550.59

What is the total amount withdrawn? = $550.59*5*12 = $33035.4