# Thread: Help with annuities due.

1. ## Help with annuities due.

Also ya know show me the formulas for annuities due?

The instructions in the book are: Find the amount of the following annuities due if interest is compounded annually. Find the amount of interest earned.

R= $1200 i=o.075 n=8 Answer in back of book$13,475.82
$3875,82 R=$17544 i=0.08 n=10
$138,997.66$33,733.66

2. ## Re: Help with annuities due.

i would hope these formulae are in your textbook.

Notation varies by country and teacher, the formulae i was taught are:

Definitions
i = interest rate (compounded once per period)
n = number of periods
S = total payment per period
FV = future value
d = rate of discount

formulae
$\displaystyle d = \frac{i}{1+i}$
$\displaystyle FV = S \frac{(1+i)^n - 1}{d}$

subbing your numbers in (i assume R was the annual payment):
$\displaystyle d = 0.075/1.075 = 0.069767$
$\displaystyle FV = 1200 \times \frac{1.075^8 - 1}{0.069767} = 13475.82$

Now, for the interest earned. The final value must be equal to the Cash invested plus interest., so

13475.82 = (cash invested) + (interest paid)

You know that the cash invested is 1200*8, so:

$\displaystyle 13475.82 = 1200 \times 8 + (interest~paid)$
$\displaystyle 3875.82 = (interest~paid)$

You try the other one.

A more detailed overview of annuity formulae is here if required:
http://www.mathhelpforum.com/math-he...gfan+annuities

3. ## Re: Help with annuities due.

So what's the formula for interest earned? I forget which is the interest paid and how to do so and I couldn't find it in that link you provided.

4. ## Re: Help with annuities due.

Originally Posted by SpringFan25
Now, for the interest earned. The final value must be equal to the Cash invested plus interest., so

13475.82 = (cash invested) + (interest paid)

You know that the cash invested is 1200*8, so:

$\displaystyle 13475.82 = 1200 \times 8 + (interest~paid)$
$\displaystyle 3875.82 = (interest~paid)$
as above