formulating exponential equations

[cycyuts]

Most investments receive compound interest. This allows an investment to earn interest already received. Miranda plans to invest $5000. Find the value of the investment after one year, given the following rates:

a. Annual interest of 12% compounded monthly

b. Annual interest of 8% compounded quarterly (4 times per year)

c. Annual interest of 5.2% compounded weekly.


Help would be much appreciated.
So far for problem letter a. I have f(x)=5000(1+(1.12/12))^x where after one year there is , but every time I try it the answer is wrong. Would anybody be able to help? I f so it'd be much appreciated. The answers are already given, but I need to know to get the problems correct.



Answer key----------------------------------------

a. $5634.13

b. $5412.16

c. $5266.74

 

[Deleted member 4993]

Most investments receive compound interest. This allows an investment to earn interest already received. Miranda plans to invest $5000. Find the value of the investment after one year, given the following rates:

a. Annual interest of 12% compounded monthly

b. Annual interest of 8% compounded quarterly (4 times per year)

c. Annual interest of 5.2% compounded weekly.


Help would be much appreciated.
So far for problem letter a. I have

f(x)=5000(1+(1.12/12))^x <<< What does 'x' stand for??

Interest after 1 year = 5000*(1 + 0.12/12)[sup:3feeexsz]12[/sup:3feeexsz] - 5000


where after one year there is , but every time I try it the answer is wrong. Would anybody be able to help? I f so it'd be much appreciated. The answers are already given, but I need to know to get the problems correct.



Answer key----------------------------------------

a. $5634.13

b. $5412.16

c. $5266.74

 

[Denis]

I have f(x)=5000(1+(1.12/12))^x where after one year there is , ...

Where in heck did you get that?!
Don't use f(x); use FV (Future Value):
FV = 5000(1 + .12/12)^12 = 5634.125151...
Do the others similarly...

 

[Mrspi]

Most investments receive compound interest. This allows an investment to earn interest already received. Miranda plans to invest $5000. Find the value of the investment after one year, given the following rates:

a. Annual interest of 12% compounded monthly

b. Annual interest of 8% compounded quarterly (4 times per year)

c. Annual interest of 5.2% compounded weekly.


Help would be much appreciated.
So far for problem letter a. I have

f(x)=5000(1+(1.12/12))^x <<< What does 'x' stand for??

Interest after 1 year = 5000*(1 + 0.12/12)[sup:ieipa5iy]12[/sup:ieipa5iy] - 5000 I disagree with this. The question asks for the amount IN THE ACCOUNT at the end of 1 year


where after one year there is , but every time I try it the answer is wrong. Would anybody be able to help? I f so it'd be much appreciated. The answers are already given, but I need to know to get the problems correct.



Answer key----------------------------------------

a. $5634.13

b. $5412.16

c. $5266.74

Formula for compound interest....

A = ending amount in account
P = amount invested
r = interest rate expressed as a decimal (i. e. 5% would be 0.05)
n = number of times interest is paid in a year
t = number of years

A = P * [1 + (r/n)]^(n*t)

Let's look at part (a).
if you start with $5000, that would be P. And if the interest rate is 12%, we'd write that as 0.12. If the interest is compounded MONTHLY, interest would be paid 12 times in a year, and that is "n"

If you do this for 1 year, then t = 1.

Ok...substitute into the formula:

A = 5000* [1 + (0.12/12)]^(1*12)

Do the arithmetic...I used a calculator. And I got this:

A = 5634.125151

Or, A = 5634.13

You'll have $5634.13 in the account after 1 year.

Now...try it yourself for the remaining parts of the problem. If interest is compounded quarterly, how many interest period would there be per year? (that's what you would use for "n" in part b). For part c, interest is compounded weekly...how many times would it be compounded in a year?

See what you can do with the remaining parts of the problem.