|
Question 498977: You have $1000 to start a retirement account. The 1st month, you deposit $1000, plus your new monthly deposit amount of $150. Then every month you deposit the $150 in a retirement account earning 3.8% interest compounded monthly. If there are 20 years until you retire, how much will you have? How much will you have if you retire in 30 years?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! time point 0 you deposit $1150
time point 1 through n you deposit $150
each time point is another year.
time point 1 is the end of the first year.
time point 2 is the end of the second year.
etc.
the interest rate is 3.8% per year compounded monthly.
3.8% is .038 annual interest rate.
divide that by 12 to get .00316666667 interest rate per month.
you have 2 equations that will provide you with the results you want.
the first equation is the future value of a present amount.
the second equation is the future value of a payment.
those formulas can be found at the following address:
http://www.algebra.com/algebra/homework/Finance/FINANCIAL-FORMULAS-101.lesson
those formulas will provide you with the following results after you provide them with the necessary information.
for 20 years in the future:
the future value of a present amount formula requires:
PA = 1150
i = .00316666667
n = 12 * 20 = 240
the future value of a payment formula requires:
PMT = 150
i = .00316666667
n = 12 * 20 = 240
for 30 years in the future:
same information except:
n = 12 * 30 = 360 in both formulas.
the answers you get should be the following:
future value of a present amount for 20 years = $2,456 rounded to the nearest dollar.
future value of a payment for 20 years = $53,797 rounded to the nearest dollar.
future value of a present amount for 30 years = $3,589 rounded to the nearest dollar.
future value of a payment for 30 years = $100,475 rounded to the nearest dollar.
you add the future value of a present amount and the future value of a payment together to get:
20 year future value = $56,252.86 rounded to the nearest penny.
30 year future value = $104,064.44 rounded to the nearest penny.
|
|
|
| |
