Question

In: Finance

You have been saving $100/month for the last 10 years in a retirement account that earns...

You have been saving $100/month for the last 10 years in a retirement account that earns 1% interest monthly.

(a) How much money do you have in your retirement account today? (25 points)

(b) If you STOP making contributions to your retirement account, but leave the amount you currently have in it to continue earning interest at 1% per month, how much money will you have in your retirement account when you retire in 30 years? (20 points)

(c) You expect to live another 25 years after you retire. Your plan is to make equal monthly withdrawals from your retirement account over this 25-year retirement period such that the account is fully exhausted. How much money can you withdraw each month? Assume that you continue to earn 1% per month on your retirement savings. (20 points)

Solutions

Expert Solution

Answer (a):

Monthly savings = $100

Monthly interest = 1%

Number of months = 10 * 12 = 120 months

For ordinary annuity:

FV = Periodic annuity * ((1 - Periodic Interest rate) Number of periods - 1)1/ Periodic Interest rate

= 100 * ((1 + 1%) 120 - 1) /1%

= $23,003.8689

Amount in your retirement account today = $23,003.87

Answer (b):

Number of months = 30 * 12 = 360

FV = PV * (1 + Periodic interest rate) Number of periods

= 23003.8689 * (1 + 1%) 360

= $826980.84

Money you will have in your retirement account when you retire in 30 years = $826,980.84

Answer (c)

Number of months (retirement period) = 25 * 12 = 300

The question does not tell whether withdrawal is done at beginning of month or at the end of month.

Hence two answers are given.

(i) In case withdrawal is done at the beginning of month:

Money you can withdraw per month = PMT(rate, nper, pv, fv, type)

= PMT(1%, 300, -826980.84,0,1)

= $8,623.72

Money you can withdraw per month if drawn at beginning of month = $8,623.72

(ii) In case withdrawal is done at the end of each month:

Money you can withdraw per month = PMT(rate, nper, pv, fv, type)

= PMT(1%, 300, -826980.84,0,0)

= $8,709.96

Money you can withdraw per month if drawn at the end of month = $8,709.96


Related Solutions

Suppose you want to have $800,000 for retirement in 25 years. Your account earns 5% interest....
Suppose you want to have $800,000 for retirement in 25 years. Your account earns 5% interest. a) How much would you need to deposit in the account each month? $ 1,343.39 Correct b) How much interest will you earn? $
Suppose you want to have $500,000 for retirement in 35 years. Your account earns 4.3% interest....
Suppose you want to have $500,000 for retirement in 35 years. Your account earns 4.3% interest. How much would you need to deposit in the account each month? Round your answer to the nearest cent as needed. $ How much would you need to deposit in an account each month in order to have $20,000 in the account in 9 years? Assume the account earns 2.6% interest. You have $500,000 saved for retirement. Your account earns 6.4% interest. How much...
Suppose you want to have $400,000 for retirement in 30 years. Your account earns 5% interest....
Suppose you want to have $400,000 for retirement in 30 years. Your account earns 5% interest. a) How much would you need to deposit in the account each month? b) How much interest will you earn? You deposit $2000 each year into an account earning 6% interest compounded annually. How much will you have in the account in 35 years? A man wants to set up a 529 college savings account for his granddaughter. How much would he need to...
FINANCE: 2. Suppose you want to have $800,000 for retirement in 20 years. Your account earns...
FINANCE: 2. Suppose you want to have $800,000 for retirement in 20 years. Your account earns 7% interest. a) How much would you need to deposit in the account each month? $ b) How much interest will you earn? $ c) Suppose you waited 10 years to invest in the same retirement fund and have the same $800,000 for retirement at the same 7% interest. What amount will you have to deposit each month to match the value of your...
Suppose you want to have $800,000 for retirement in 35 years. Your account earns 7% interest....
Suppose you want to have $800,000 for retirement in 35 years. Your account earns 7% interest. a) How much would you need to deposit in the account each month? $ b) How much interest will you earn? $
Suppose you want to have $500,000 for retirement in 20 years. Your account earns 5% interest....
Suppose you want to have $500,000 for retirement in 20 years. Your account earns 5% interest. How much would you need to deposit in the account each month?
suppose you want to have 700,000 for retirement in 35 years. your account earns 9% interest....
suppose you want to have 700,000 for retirement in 35 years. your account earns 9% interest. a how much would you need to deposit in the account each month? b how much interest will you earn
Suppose you want to have $700,000 for retirement in 25 years. Your account earns 7% interest...
Suppose you want to have $700,000 for retirement in 25 years. Your account earns 7% interest compounded monthly. a) How much would you need to deposit in the account each month? $ b) How much interest will you earn? $
You wish to have $10 million in your retirement account at the end of 40 years....
You wish to have $10 million in your retirement account at the end of 40 years. You can invest at an annual return of 10 percent per year. a) How much should you deposit every year over the next 40 years to meet your goal? b) How much can you withdraw per year for 30 years after retirement? c) How much can you withdraw for 30 years after retirement if you wish to leave your family with a lump sum...
You are planning your retirement in 10 years. You currently have $164,000 in a bond account...
You are planning your retirement in 10 years. You currently have $164,000 in a bond account and $604,000 in a stock account. You plan to add $7,600 per year at the end of each of the next 10 years to your bond account. The stock account will earn a return of 10.5 percent and the bond account will earn a return of 7 percent. When you retire, you plan to withdraw an equal amount for each of the next 21...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT