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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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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 = ,
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 = = 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 = .
From this equation we get the ANSWER
A = = 11363.48.
So, the present value of this ordinary annuity is $11363.48. ANSWER
On Ordinary Annuity saving plans see the lessons
- Ordinary Annuity saving plans and geometric progressions
- Solved problems on Ordinary Annuity saving plans
- Finding present value of an annuity, or an equivalent amount in today's dollars
in this site.
The lessons contain EVERYTHING you need to know about this subject, in clear and compact form.
On discretely compounded accounts, see the lessons
- Compound interest percentage problems
- Problems on discretely compound accounts
in this site.