What is the future value of $250,000 invested at a continuously compounded annual rate of 5%, after 3 years?

Question

Round to the nearest dollar

Answer 1

Given:P=$250,000
R=5%
T=3 YEARS.AND COMPOUNDING IS EVERY YEAR.
Let us calculate future value after 1 year.
Interest=P*R*T/100
=250000*5*1/100
=12500$
PRINCIPLE AMOUNT FOR SECOND YEAR=250000+12500=262500$
Let us calculate future value after 2 ND year.
Interest=P*R*T/100
=262500*5*1/100=13125$
PRINCIPLE AMOUNT FOR 3RD YEAR=262500$+13125$=275625$
Let us calculate future value after 3RD year.
Interest=P*R*T/100=275625*5*1/100=13781.25
SO,TOTAL AMOUNT AFTER 3 YEARS=289406.25$

Answer 2

Let P= the amount of the investment=$250,000

At the end of the first year, the investment P including interest will amount to:

P+Pi where i is the compounded annual rate

Factoring out P from the above expression, we get:

P(1+i)

At the end of the second year, the investment P will amount to:

P(1+i)+ P(1+i)i

Factoring out P(1+i) from the above expression we get:

P(1+i)(1+i)= P(1+i)^2

At the end of the third year, the investment P including interest will amount to:


P(1+i)^2+(P+i)^2i

Factoring out P(1+i)^2 from the above expression we get:

P(1+i)^2(1+i)=

P(1+i)^3

Now substitute in the above expression the given value of P and i:

250000(1+5/100)^3=
250000(1+.05)^3=
250000(1.05)^3=
250000(1.157625)=
$289,406.25

Note that 5% can be written as 5/100 or .05.

If you noticed we have derived a compound interest formula. For an investment P at an annual interest rate i , at the end of n years, the total investment will amount to
P(1+i)^n. In the above problem n=3.

But if deriving a formula is too much for you, then solve the problem step by step, i.e. at the end of the 1st year, how much will the total investment be; at the end of the 2nd year, how much will the total investment be; and at the end of the 3rd year, how much will the investment be.

That will be a very tedious process. Can you imagine how long it will take you to solve a problem if say the number of years is changed to 10 instead of 3? So, simplify and learn to derive a formula.

Answer 3

A=p(1+r/100)^n
=250000(1+.05)^3
=250000*1.05^3
=289406.25$

Answer 4

Amount= P(1+R/100)*n
= 250000(1+5/100)*3
= 250000(1+0.05)*3
= 250000(1.05)*3
= 250000X1.157625
= 2892406.25
= $2,892,406(approx)

Answer 5

the equation for continually compounded activity is pe^(rt) equals the resultant money p could be the quantity you commence with it would desire to be capital P e is a relentless r is the activity fee t is time in years so pretend you have $a million so which you will desire to double that it is going to become $2 so the equation could be 2=1e^(r7) organic log the two facets ln 2=lne^(r7) then making use of log regulations 7r could be moved next to ln e ln2=(7r)lne lne is comparable to a million ln2=7r divide by potential of seven r=.09902 multiply by potential of a hundred to make it right into a %

Answer 6

Continous Compound Interest Formula
I = Pe^(rt)

I = 250000 * e^(.05 * 3)
I = 250000 * e^(.15)
I = $290459

Answer 7

Thankyou for the answers everyone <3

Answer 8

The answer is 250000*(1.05^3)=$289,406

Answer 9

$290,459 is the nearest integer to 250,000 * exp(0.05 * 3) = 290,458.56....

Answer 10

its 250000 * e^(0,15) = 290458,5607


In general: Investment * e^(interest rate * years)