Question 1201579
.
Helen will be investing an amount of $3900 annually at the end of each of the following 
four years. She will earn compounded interest of 14% per annum. 
Calculate the present value of Helen’s investment.
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<pre>
This saving plan of depositing $3900 annually at the end of each of the following 4 years 
at a yearly interest rate of 14%, compounded annually, is called an ORDINARY ANNUITY plan.


There is a formula to calculate the total amount which the plan generate at the end.


The formula is

    f = {{{p * (((1 + r) ^ n-1)/r)}}},


f is the future value;
p is the regular payment at the end of each time period (yearly payment in this case);
r is the interest rate per time period;
n is the number of time periods.


In your problem


time periods are years;
p = 3900 dollars;  
r = 0.14 per year;
n = 4 years.


Formula becomes f = {{{3900*(((1 + 0.14)^4-1)/0.14)}}} = 19192.46 dollars (rounded).


Now, the problem asks, what amount A should be deposited one time today
on the 4 years account giving 14% interest rate annually and compounded annually,
in order for to get the same total of $19192.46 at the end of 4 years?


To determine it, we write this equation for the unknown principal amount A

    19192.46 = {{{A*(1+0.14)^4}}}.


From this equation we get the <U>ANSWER</U>

    A = {{{19192.46/(1+0.14)^4}}} = 11363.48.


So, the present value of this ordinary annuity is  $11363.48.    <U>ANSWER</U>
</pre>


On &nbsp;Ordinary &nbsp;Annuity saving plans see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Ordinary-Annuity-saving-plans-and-geometric-progressions.lesson>Ordinary Annuity saving plans and geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Solved-problem-on-Ordinary-Annuity-saving-plans.lesson>Solved problems on Ordinary Annuity saving plans</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Finding-present-value-of-an-annuity.lesson>Finding present value of an annuity, or an equivalent amount in today's dollars</A> 

in this site.


The lessons contain &nbsp;EVERYTHING &nbsp;you need to know about this subject, &nbsp;in clear and compact form.



On discretely compounded accounts, &nbsp;see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/percentage/lessons/Compound-interest-percentage-problem.lesson>Compound interest percentage problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/Problems-on-discretely-compound-accounts.lesson>Problems on discretely compound accounts</A> 

in this site.