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December 26, 2014

December 26, 2014

Posted by **Andrea** on Wednesday, December 12, 2012 at 10:50am.

- algebra -
**MathMate**, Wednesday, December 12, 2012 at 11:27amFormula for continuous interest:

A=Pe^(rt)

take log on both sides and solve for r:

r=ln(A/P)/t

where A=4300000000,P=0.93,t=1000

You should get around 2.2%, ASSUMING banks do not round interest deposits to the nearest cent.

If they deposit interest every two months and round the interest to the nearest cent, the money will not grow at all because interest for every 2 months is less than half a cent.

If it had been compounded quarterly, then the formula is

A=P(1+(r/4))^(4t)

Again, take log on both sides,

log10(A/P)=(4t)log10(1+r/4)

=>

r = (10^[log10(A/P)/(4t)]-1)*4

where log10=log to the base 10

A=4300000000

P=0.93

t=1000 (years)

You should get also about 2.2%, but a little less than continuous interest.

Again, it depends on how banks "round" down or round up the cent, and hope they don't have monthly charges! :)

- algebra -
**Reiny**, Wednesday, December 12, 2012 at 11:33amcontinuous growth:

4300000= .93 e^1000r

4623655.91 = e^1000r

1000r = ln 4623655.91

r = .0153467

= 1.535%

compounded quarterly:

let the quarterly rate be i

.93(1+i)^4000 = 4300000

(1+i)^4000 = 4623655.91

i+i = 1.003844...

i = ..003844..

so the annual rate compounded quarterly is .. 0.015376 or 1.5376 %

check:

.93 e^(.01535(1000)) = 4, 314,230 using the rounded continuous rate

.93(1+.003844)^4000 = 4,299,999.76 not bad!

- algebra -
**MathMate**, Wednesday, December 12, 2012 at 10:48pmAndrea, which continent are you on?

In USA, 1 billion = 10^9, and I think in UK and France, 1 billion = 10^12. This makes a big difference.

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