Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 261

Compound Interest (finding the value of n)

Fearne invests £5600 in a savings account.
She gets 2% per annum compound interest.
After n years, Fearne has £6061.62 in her account.
Work out the value of n.

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I found finding the value of n one way straightforward. I put 5600 into my calculator, pressed equal then pressed ANS to store it. Then put the multiplier (1.02, for the 2% interest) next to ANS in brackets. Then pressed = repeatedly until I got my answer of 6061.62. As I had to press it 4 times this told me n=4.

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But before doing that I wrote out the following equation;
5600(1.02)^n=6061.62
(1.02)^n=6061.62/5600
(1.02)^n=1.082432143
1.02=nth root of 1.082432143
Nb; I wasn’t sure of this last step but it seemed to check out re;
2^2=4
Therefore;
Sqrt4=2
And then I substituted the 4 (from my first answer using the calculator) for the n and that checked out;
1.02=4th root of 1.082432143

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My question;

How do I get the nth root from the second method, once I’ve got to the stage;
1.02=nth root of 1.082432143 ?
Is there a way, other than putting the 5600 into the calculator and multiplying it by 1.02 repeatedly?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,524

Re: Compound Interest (finding the value of n)

Yes if you use logs.

You can have logs in base 10 or the natural log base (e) but both logs have to use the same.

Bob

Using 1.08 I calculated n as 3.99999999 in Excel so that seems ok.

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 261

Re: Compound Interest (finding the value of n)

Thanks, Bob.

Would that be AS, or A, level maths? Or further on than that?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,524

Re: Compound Interest (finding the value of n)

When I was at school we did tricky multiplications and divisions using log tables so we learnt it earlier than that ie O level stage.  Nowadays it's probably AS.

I can show you the underlying theory if you wish.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 261

Re: Compound Interest (finding the value of n)

Thanks, Bob.

Not now though, although I will take up your offer later. Cheers.