# Finance Question

• Aug 25th 2007, 08:05 PM
walrusdealer
Finance Question
Hey all, I've got a question about a finance question i cant seem to get my head around.

We've been given a job in which we earn \$53823.43 p/yr (or 4485.30 p/month)

a) The money that you save over three years will form the deposit on a home. Assuming that over three years your salary does not increase, that you are going to save 15% of your gross monthly income (rounded to the nearest \$10) at the start of each month, and that the money you save earns 6% interest compounding monthly, show all working to determine the total amount that you will save in this time. any assumptions must be stated.
Show also how the calculator (casio fx9860G) may be used to check your answer.

b) Now assuming that your salary increases by 4% p.a, that you are going to save 15% of your gross monthly income (rounded to the nearest \$10) at the start of each month, and that the money you save earns 6% interest compounding monthly, show all working to determine the total amount that you will save in three years
• Aug 25th 2007, 08:20 PM
TKHunny
Quote:

Originally Posted by walrusdealer
We've been given a job in which we earn \$53823.43 p/yr (or 4485.30 p/month)

a) The money that you save over three years will form the deposit on a home. Assuming that over three years your salary does not increase, that you are going to save 15% of your gross monthly income (rounded to the nearest \$10) at the start of each month, and that the money you save earns 6% interest compounding monthly, show all working to determine the total amount that you will save in this time. any assumptions must be stated.
Show also how the calculator (casio fx9860G) may be used to check your answer.

b) Now assuming that your salary increases by 4% p.a, that you are going to save 15% of your gross monthly income (rounded to the nearest \$10) at the start of each month, and that the money you save earns 6% interest compounding monthly, show all working to determine the total amount that you will save in three years

First:

0.15*4485.30 = 672.795, so we're saving 670/month for 3 years. Do you have an accumulation formula for that? Will you be doing it from basic principles?

Second:

672.795*1.04 = 699.7068 ==> 700/mo
699.7068*1.04 * 727.695 ==> 730/mo

This time, we're doing EXACTLY what we did in the first problem and then adding two pieces:

1) 30/month for 2 years and
2) 30/month for 1 year.

This is my favorite part of this problem: "show all working" Let's see what you get.
• Aug 25th 2007, 08:27 PM
walrusdealer
Quote:

Originally Posted by TKHunny
First:

0.15*4485.30 = 672.795, so we're saving 670/month for 3 years. Do you have an accumulation formula for that? Will you be doing it from basic principles?

Second:

672.795*1.04 = 699.7068 ==> 700/mo
699.7068*1.04 * 727.695 ==> 730/mo

This time, we're doing EXACTLY what we did in the first problem and then adding two pieces:

1) 30/month for 2 years and
2) 30/month for 1 year.

i think we're allowed to use a geometric progression formula, but im not entirely sure how to apply it to it.
^^^
im pretty sure thats the one he wants us to use

do you know of any other "accumulation" formulas?

apparently we also have to "prove" the formula
and do you know how i could show that the answer can be checked on the calculator?
thankyou ^_^
• Aug 26th 2007, 07:26 PM
TKHunny
There's a simple trick for that proof. It's not entirely satisfying ,but it does provide a good level of assurance.

Here's the series.

1 + r + r^2 + r^3 + ... + r^n

Just give it a sum.

1) 1 + r + r^2 + r^3 + ... + r^n = S

Multiply it all by r.

2) r + r^2 + r^3 + ... + r^n + r^(n+1) = Sr

Subract 2) from 1)

1 - r^(n+1) = S - Sr

Can you solve that for S?