i need help w/ hw?

Question

I need help with my FINANCIAL MATH HW asap!?
First question is:
Suppose you invest $175 per month in an annuity that pays 7.25% annual interest, compounded monthly, and your employer matchs your investments.

A. How much will the annuity be worth in 25 years?

B. How much of that total will be money that you invested?

C. How much of the total will be money that your employer contributed?

D. How much of the total will be interest?

E. How long will it take for the annuity to be worth $1,000,000?

All your help is appreciated! thanks.

Answer 1

The formula is:

FV = P((1+r)^n-1) / r

Where FV is future value, P is amount of payment, r is the rate of return in percent (expressed as a decimal), so in this case it is .0725, and n is the number of periods.

You have 12 periods in a year, so your interest rate for this calculation will be .0725/12 or .0060. Also, you want over 25 years, so that is 12 periods x 25 years = 300 periods.

Okay.

FV = P((1+r)^n-1) / r

($350 since that's $175 x 2--the employer is matching)

= $350 ((1+.006)^300-1) / .006

= $350 (6.017 -1) / .006

= $350 (5.017/ .006)

= $292, 658

Rounding can cause large errors, so recalculate using the # of decimal places you want.

B. Your investment would be:

$175 x 12 x 25 = $52,500

C. The same amount

D. Difference between total result of the annuity and 2 x $52,500

E. Here you have to take the formula and rework it to get an exact answer. Using the "Rule of 72 though" you can take an interest rate, divide it into 72, and that will be approximately how long it would take to double your money.

It took 25 years to make approx 300,000. 72/7.25 = 9.93 years, or about 10 years. So, 35 years to 600,000 and then less than 45 to 1,000,000.

Have fun!

Mysstere