Compounding daily interest

[hftransit]

Hello everybody,

I am wanting to know how much $1,000 will be after 2,600 days at 1% compounding interest per day - and can you please tell me the answer in both numbers and words?

Thank you very very kindly,
Harold

 

[chrisr]

1% interest is 0.01 of the "daily" amount.

After 1 day, the amount has grown to (1000)+0.01(1000)=1000(1.01)
1% interest is generated on this increased amount in the 2nd day.

After 2 days, the amount has grown to $\displaystyle 1000(1.01)+0.01[(1000)(1.01)]=1000(1.01)^2$

The pattern is....

the power corresponds to the number of elapsed days,

hence after 2600 days, the amount is destined to have grown to

$\displaystyle 1000(1.01)^{2600}\ dollars$

 

[masters]

1% interest is 0.01 of the "daily" amount.

After 1 day, the amount has grown to (1000)+0.01(1000)=1000(1.01)
1% interest is generated on this increased amount in the 2nd day.

After 2 days, the amount has grown to $\displaystyle 1000(1.01)+0.01[(1000)(1.01)]=1000(1.01)^2$

The pattern is....

the power corresponds to the number of elapsed days,

hence after 2600 days, the amount is destined to have grown to

$\displaystyle 1000(1.01)^{2600}\ dollars$

Chrisr: $\displaystyle 1000(1.01)^{2600}\approx$$172,017,184,400,000

Hello everybody,

I am wanting to know how much $1,000 will be after 2,600 days at 1% compounding interest per day - and can you please tell me the answer in both numbers and words?

Thank you very very kindly,
Harold
Hello everybody,

I am wanting to know how much $1,000 will be after 2,600 days at 1% compounding interest per day - and can you please tell me the answer in both numbers and words?

Thank you very very kindly,
Harold

Hi hftransit,

Using the compound interest formula:

$\displaystyle A=P\left(1+\frac{r}{n}\right)^{nt}$

t = the number of years so 2600 days is approx 2600/365 years.

n = the number of compounding periods in each year

$\displaystyle A=1000\left(1+\frac{.01}{365}\right)^{365\cdot\frac{2600}{365}}$

Comes out to about $1,074.

 

[chrisr]

I'm always getting caught out with that annual conversion!
still, it would have been a nice bit of profit,
sorry, I'm just back from 14 hours on the road.

 

[chrisr]

1% per year is $\displaystyle \frac{1}{365}$% per day.

Then, after 1 day, the amount has grown to

$\displaystyle 1000+\frac{0.01}{365}(1000)=1000(1+\frac{0.01}{365})$ dollars

After 2 days, this has grown to

$\displaystyle 1000(1+\frac{0.01}{365})+\frac{0.01}{365}(1000)(1+\frac{0.01}{365})$

$\displaystyle =1000(1+\frac{0.01}{365})^2$

The pattern is..... number of days elapsed = index

Therefore after 2600 days,
the money ought to have increased to

$\displaystyle 1000(1+\frac{0.01}{365})^{2600}$ dollars

Thanks masters!!