SOLUTION: 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

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

RELATED QUESTIONS
tom saves $300 at the end of each month for 20 years. he invests the money at 14% a... (answered by ptfile)

Zach invests $4000, part of it at 10% annual interest and the rest at 12% annual... (answered by elima)

Rodrigo invests $4000, part of it at 10% annual interest and the rest at 12% annual... (answered by greenestamps,ikleyn)

A person invests $50,000 for one year; some is invested at 7%, some at 8%, and the... (answered by mananth)

At the beginning of each year, Joe invests $10,000 in his retirement fund. The fund gives (answered by jorel555)

a man invests $50 at 10% compound interest. how much will he have at the beginning of the (answered by stanbon)

At the beginning of each year, Jerome invests $1,400 semiannually at 8% for nine years.... (answered by ikleyn)

If someone invests $3000 at 5% annual interest and $4000 at 6% annual interest, how much... (answered by stanbon)

A student invests $5,500 at 5% and 6% annually. After one year, the student receives a... (answered by dkppathak)