How much money invested at 10% compounded continuously for 5 years will yield $610?

Question

Please help...Giving the answer is ok but answer with explanation would be better...thanks

Answer 1

Continuous compounding uses the e^x form.

So you know t=5 and A(5) = 610 and r = .1

The formula is:

A(t) = A(0)e^(rt)


So

A(5) = 610 = A(0) e^(.1(5)) = A(0) e^(.5)

Divide both sides by e^(5.5) and you get your answer:

A(0) = 610 / e^(.5) = 369.98

So it appears that you'd have to deposit $369.98.

Answer 2

The equation you would use is 610=A(e to the R*T power). "e" is a statistical number (approximately 2.71828182845...). So, the calculation is the interest times the number of years (10%*5years) which gives you how many times e must be exponentially timed out by. This gives you 1.6487212. The problem now looks like this:

610=A*1.6487212

Divide 610 by 1.6487212 and you get the amount needed. The answer to the problem then is $369.98 (rounded down to the nearest cent). It has been about three years since I've done any calculus or statistics, but that should be right. the breakdown of the problem is:

610=A(2.71828182845 to the [10%*5] power)
610=A(2.71828182845 to the .5 power)
610=A*1.6487212
A=610/1.6487212
A=369.98371829...

Answer 3

I am going to assume that by "compounded continuously" you are referring to simple interest.

Simple interest:

P * R * Y = I

P = Principal
R = Rate
Y = Years
I = Interest

Your problem has a bit of a quirk, because they have given you the total yield, not just the interest yield. Total yield equals Interest + Principal.

Therefore:

P + I = 610

I = 610 - P

Substitute this into the original equation, along with your given values:

P * .10 * 5 = 610 - P
P * .5 = 610 - P
P = 1220 - 2p
3 * P = 1220
P = 1220/3 or $406.67

Plug back into original equation to check:

$406.67 * .10 * 5 = $203.34

$203.34 + $406.67 = $610.01

It's a penny off due to rounding.

HOWEVER

If the $610 they are referring to is a total interest yield of $610, then:

P * .10 * 5 = 610

Solving for P in this case would be $1220.

You'd have to find out whether "yield" means total interest yielded, or if yield refers to Principal PLUS interest.

Answer 4

P=F(P/F, 10%, 5)
P=610(P/F,10%,5)
=610*0.6209
=$378.75 Ans.

Answer 5

610 = Pe^((.1)(5))

P = 610/e^((.1)(5))

P = $369.98

Answer 6

610=pe^.5=1.6487212707001281468486507878142p
p=610/1.6487212707001281468486507878142=$370