# compound interest

• Aug 26th 2012, 02:45 PM
mathsgirl123431
compound interest
Compound interest is interest paid on an amount and on the interest already received on that amount. You can solve compound interest questions using the formula :

A = P ( 1 + R divided by 100 ) to the power of n

where P is the amount invested initially
R is the rate of interest (percentage per year)
n is the number of years invested
A is the amount in the account at the end of ten years

A building society pays compound interest at a fixed rate of 3.5% per annum. £2000 is invested initially in an account.

What will be the value at the end of 5 years?
After how many whole years will the value of the account first reach £3000?

So is the solution: 2000 (1 + 3.5 divided by 100 ) power of 5 = £2375.37

And 12 years

(Happy)
• Aug 26th 2012, 02:49 PM
MaxJasper
Re: compound interest
£2375.37 is correct.
After 12 whole years value will be £3022.14
• Aug 26th 2012, 05:21 PM
Wilmer
Re: compound interest
Quote:

Originally Posted by mathsgirl123431
A = P ( 1 + R divided by 100 ) to the power of n
where P is the amount invested initially
R is the rate of interest (percentage per year)
n is the number of years invested
A is the amount in the account at the end of ten years : .....end of n years !

In the standard formula, r / 100 is shown as i :
A = P(1 + i)^n

Isolating n: n = LOG(A/P) / LOG(1 + i)

So the 3000 is reached in ~11.786 years (not 12)
LOG(3000/2000) / LOG(1.035) = 11.786....

WHAT is your question anyway? I see none...
• Aug 26th 2012, 05:52 PM
HallsofIvy
Re: compound interest
Quote:

Originally Posted by mathsgirl123431
Compound interest is interest paid on an amount and on the interest already received on that amount. You can solve compound interest questions using the formula :

A = P ( 1 + R divided by 100 ) to the power of n

where P is the amount invested initially
R is the rate of interest (percentage per year)
n is the number of years invested
A is the amount in the account at the end of ten years

A building society pays compound interest at a fixed rate of 3.5% per annum. £2000 is invested initially in an account.

What will be the value at the end of 5 years?
After how many whole years will the value of the account first reach £3000?

So is the solution: 2000 (1 + 3.5 divided by 100 ) power of 5 = £2375.37

And 12 years

(Happy)

No, neither of those is correct. Perhaps if you told us exactly what you did we could point out a mistake. For example in the first problem, you do want to calculate 2000(1.35)^5. But that is NOT 2375.37.
• Aug 26th 2012, 07:47 PM
Wilmer
Re: compound interest
Quote:

Originally Posted by HallsofIvy
No, neither of those is correct. Perhaps if you told us exactly what you did we could point out a mistake. For example in the first problem, you do want to calculate 2000(1.35)^5. But that is NOT 2375.37.

Halls, 2000(1.035)^5 = 2375.3726.....; so that one is correct. You're a generous Banker, paying 35% !
• Aug 26th 2012, 07:51 PM
HallsofIvy
Re: compound interest
Ouch! No wonder I'm going broke!
• Aug 28th 2012, 05:29 AM
mathsgirl123431
Re: compound interest
But the question says how many whole years, so wouldn't it be 12?
Because 11.786 isn't a whole year, and after 11 years it's not yet at £3000, or am I just overthinking the question?
• Aug 28th 2012, 06:35 AM
Wilmer
Re: compound interest
Quote:

Originally Posted by mathsgirl123431
But the question says how many whole years, so wouldn't it be 12?
Because 11.786 isn't a whole year, and after 11 years it's not yet at £3000, or am I just overthinking the question?

Whatever. I gave you the "exact" time; you're correct with 12 as "whole years".
• Aug 28th 2012, 06:55 AM
mathsgirl123431
Re: compound interest
Okay, thanks for taking the time to show me how too work it out exactly Wilmer :)