Question

FINANCE:

3.

3A.

You have $500,000 saved for retirement. Your account earns 9% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 15 years?

3B.

You want to be able to withdraw $40,000 each year for 15 years. Your account earns 7% interest.

How much do you need in your account at the beginning?

$

How much total money will you pull out of the account?

$

How much of that money is interest?

$

3C.

You want to buy a $23,000 car. The company is offering a 4% interest rate for 48 months (4 years). What will your monthly payments be?

$

Answer 1

Question 3A:

Amount of Savings = PV = $500,000

r = monthly interest rate = 9%/12 = 0.75%

n = 15*12 = 180 months

Monthly Withdrawl amount = [r*PV] / [1 - (1+r)^-n]

= [0.75% * $500,000] / [1 - (1+0.75%)^-180]

= $3750 / 0.739450566

= $5,071.33292

Therefore, Monthly withdrawl amount = $5,071.33

Question 3B:

Withdrawl amount = P = $40,000

r = interest rate = 7%

n = 15 years

Amount at beginning = P[1 - (1+r)^-n] / r

= $40,000 [1 - (1+7%)^-15] / 7%

= $40,000 * 0.63755398 / 0.07

= $364,316.56

Therefore, Amount at beginning is $364,316.56

>>>>

Total withdrawls = $40,000 * 15 = $600,000

Therefore, total amount pulled from the account is $600,000

>>>>

Amount of interest = Total money paid - Amount deposited

= $600,000 - $364,316.56 = $235,683.44

Therefore, Amount of interest is $235,683.44

Question 3C:

Loan Amount = PV = $23,000

r = monthly interest rate = 4%/12 = 0.333333%

n = 48 months

Monthly payment = [r*PV] / [1 - (1+r)^-n]

= [0.333333% * $23,000] / [1 - (1+0.333333%)^-48]

= $76.66659 / 0.14762931

= $519.318217

Therefore, Monthly payment on car is $519.32