# Thread: Help with finding FV plz!

1. ## Help with finding FV plz!

QUS:

The money that you save over the three years will form the deposit on a home Assuming that over the three years you salary does not increase, that you are going to save 15% of your gross monthly income (rounded to the nearest ten dollars) at the start of each month, and that the money that you save earns 6% interest compounding monthly, show all working to determine the total amount you will save in this time Any assumption must be stated.

Show also how the calculator may be used to check your answer.

My salary is $60,000 My solution: ( 1 + .06/12 ) x {[1 + .06/12]^36}-1 / (.06/12) x 750 =$29649.59

Could anybody please check that i did it right?

and also i have to prove this on my graphics calculator. I used the compound interest and entered

n= 36
I% = 6
PV = 0
PMT = -750
FV =
P/Y= 12

And i click the FV button and got the amount $29502.07. I found out that the calculator did it by (future value factor x payment) and did not (x 1.005). my calculator is Casio FX9850GB Does anyone have any suggestion? Do u think the calculator is not doing it properly or something? Your help will be greatly appreciated. 2. Hello, tom_asian! Your calculator is correct. . . You have an extra factor in your formula . . . The money that you save over the three years will form the deposit on a home. Assuming that over the three years you salary does not increase, that you are going to save 15% of your gross monthly income at the start of each month, and that you earn 6% interest compounded monthly, determine the total amount you will save in this time. My solution:$\displaystyle {\color{blue}\underbrace{(1 + 0.06/12)}} \times \frac{(1 + 0.06/12)^{36} - 1}{0.06/12} \times 750 \;= \;\$29,649.59$
. . . .?

This is an Annuity . . .

The formula is: .$\displaystyle A \;=\;D\,\frac{(1+i)^n - 1}{i}$

. . where: .$\displaystyle \begin{Bmatrix}D & = & \text{periodic deposit} \\ i & = & \text{periodic interest rate} \\ n & = & \text{number of periods} \\ A & = & \text{final value}\end{Bmatrix}$

Assuming that the gross monthly salary is $5,000 (you didn't mention it), . . the periodic deposit is: .$\displaystyle D \:=\:15\% \times \$5,000 \:=\:\$750$The periodic interest rate is: .$\displaystyle i \:=\:\frac{6\%}{12} \:=\:0.005$The number of months is: .$\displaystyle n \:=\:3\times12 \:=\:36$Therefore: .$\displaystyle A \;=\;750\,\frac{1.005^{36} - 1}{0.005} \;=\; 29,502.07872 \;\approx\;\$29,502.08$

3. Originally Posted by Soroban
Hello, tom_asian!

. . You have an extra factor in your formula . . .

This is an Annuity . . .

The formula is: .$\displaystyle A \;=\;D\,\frac{(1+i)^n - 1}{i}$

. . where: .$\displaystyle \begin{Bmatrix}D & = & \text{periodic deposit} \\ i & = & \text{periodic interest rate} \\ n & = & \text{number of periods} \\ A & = & \text{final value}\end{Bmatrix}$

Assuming that the gross monthly salary is $5,000 (you didn't mention it), . . the periodic deposit is: .$\displaystyle D \:=\:15\% \times \$5,000 \:=\:\$750$The periodic interest rate is: .$\displaystyle i \:=\:\frac{6\%}{12} \:=\:0.005$The number of months is: .$\displaystyle n \:=\:3\times12 \:=\:36$Therefore: .$\displaystyle A \;=\;750\,\frac{1.005^{36} - 1}{0.005} \;=\; 29,502.07872 \;\approx\;\$29,502.08$

Sorry I would just like to clarify. thanks~~
Many of my friends said that it is an annuity due, not an immediate annuity.

The formula for a future value annuity due =

(1 + i) x $\displaystyle \;D\,\frac{(1+i)^n - 1}{i}$

....

I also worked it out manually and the annuity due formula matches my manual calculation.

So could i double check with you please? thanks