|
Question 274084: Lucy invests $300 at the beginning of each month. Raymundo invests $4000 at the end of each year and Elise a single amount of $27000 (interest compounded continuously).
If the interest rate is 10.5% per year, how much will each of them have after 15 years.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! The annual interest rate is 10.5% / 100% = .095 per year.
Lucy invests $300 at the beginning of each month.
Her compounding period is monthly.
There are 12 compounding periods in the year.
Interest rate per compounding period is .095 / 12 = .0079166666666
Number of time periods is equal to number of year times number of compounding periods per year which equals 12 * 15 = 180 time period.
Future value of payments made at the end of each time period for 180 time periods with monthly compounding equals $118,784.5884
Adjust for future value of payments made at the beginning of each time period by multiplying these results by 1 + the interest rate period results in:
$118,784.5884 * 1.0079166666666 = $119,724.9664
Lucy will have $119,724.9664 at the end of the 15 years.
Raymundo invests $4000 at the end of each year.
The compounding periods are once per year so the interest rate for Raymundo is .095 per year and the number of time periods is 15.
Raymundo will have $122,160.9229 at the end of the 15 years.
Elise invests $27,000 for 15 years with continuous compounding.
The continuous compounding formula is F = P*e^(ry) where r is the annual interest rate and y is the number of year.
Annual interest rate is .095 and the number of years is 15.
Elise will have $27,000*e^(.095*15) = $112,262.1618 at the end of the 15 years.
The following information regarding future value of payments and continuous compounding might might be helpful for you to understand what is going on here.
FUTURE VALUE OF A PAYMENT
CONTINUOUS COMPOUNDING
|
|
|
| |
