math help!

hiya....I am atrocious at math and again need some help - I must sound so lazy as If i can do nothing myself - lol - but honestly It's not that - It's that I am sooo bad at math and as part of my international Alevs - it is a compulsary subject :frown:

- so if anyone is willing to help me for rep please let me know - thank you so much :tsr:

- you're always there to help!!!

Love Ladyshort

Reply 1

madhapper

yup willing to help jus post ya questions

Reply 2

Splinter

I think most ppl are willing, as madhapper said - just give us the questions

Reply 3

ladyshort4u

These are the questions - thank you so much guys...

3. A Picture Is Worth a Thousand Words
Perhaps a picture could help save someone a thousand dollars. Imagine that you are a financial consultant and you want to provide your client with graphical representations of the effects of varying different options on a mortgage. Choose a current mortgage rate to work with and provide graphs showing the effects of changing payment periods and lengths of amortization. You may decide to look at several aspects to compare the mortgages—amounts of interest paid, length of time to pay off the mortgage, principal owing at various time intervals, and so on.

4. Retirement Plans
Sara and Ritu have just finished school and have started their first full-time jobs. Sara has decided that she is going to start putting $100/month away in a Retirement Plan. Ritu thinks that Sara is crazy because Sara is only 22 and should enjoy her money now and worry about saving for retirement later. Ritu is not going to worry about saving money until she is 45.
(a) Suppose both young women retire at age 60. How much money will Ritu have to contribute monthly, to retire with the same savings as Sara? Assume that they can invest their money at 9% compound monthly.
(b) Write a convincing argument for one of the young women’s positions.

Reply 4

Expression

ladyshort4u

4. Retirement Plans
Sara and Ritu have just finished school and have started their first full-time jobs. Sara has decided that she is going to start putting $100/month away in a Retirement Plan. Ritu thinks that Sara is crazy because Sara is only 22 and should enjoy her money now and worry about saving for retirement later. Ritu is not going to worry about saving money until she is 45.
(a) Suppose both young women retire at age 60. How much money will Ritu have to contribute monthly, to retire with the same savings as Sara? Assume that they can invest their money at 9% compound monthly.
(b) Write a convincing argument for one of the young women’s positions.

*Financial Management Hat*

First job is to check the amount that the 9 % compound interest per month is worth per annum.

Let R be the annual rate of interest, then:

[(1 + \frac{R}{12})^{12}] -1 = 0.09 \text (9 %)

A little bit of algebraic manipulation results in R = 0.086487879 = 0.0865 = 8.65 % (2dp).

Sara is investing for (60 - 22) = 38 years = 38 * 12 = 456 months.

456 * $100 per month = $45,600 total invested.

To find the future value of this after the compound interest, use a standard formula:

\mathrm{FV}(i,n) \mathrm{ = [A(1 + }i\mathrm{)^n}]

where A is the inital amount invested, i is the rate of interest per annum, and n is the number of years invested for at that rate of interest.

Substituting:

A = 45,600
i = 0.0865
n = 38

The FV = $45,600[(1.0865)^38]
= $1, 066, 828 . 50

Sara has a retirement fund of $1.0668285m

Ritu invests for 60-45 = 15 years = 180 months, at the same rate of interest = 0.0865 = 8.65 % per annum.

Working backwards from the formula above, we are looking for A, such that A*[(1.0865)^15] = $1, 066, 828 . 50

A = $1,066,828.50/(1.0865^15)
= $307,360. 9214 over 15 years.
= $1,707. 56 per month (180 months).