Help with annuities due.

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Dec 6th 2011, 11:39 AM
Johnnytest20

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
Answer in back of book
$138,997.66
$33,733.66
Dec 6th 2011, 11:48 AM
SpringFan25

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

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

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:

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

You try the other one.

A more detailed overview of annuity formulae is here if required:
http://www.mathhelpforum.com/math-he...gfan+annuities
Dec 7th 2011, 09:27 AM
Johnnytest20

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.
Dec 7th 2011, 10:03 AM
SpringFan25

Re: Help with annuities due.

Quote:

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:

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

as above