Question

Brian invests £7500 into his bank account.

He receives 6% per year compound interest.
How many years will it take for Brian to have more than £10000?

please i b e g

Answer 1

Here is my written solution, I hope it helps you :)

Alternatively to this you could use the equation of 7500 x 1.06^t and use trial and error by replacing the value of t until you go beyond £10000.

Answer 2

Answer: 5 years

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Work Shown:

`A = P*(1+r/n)^(n*t)\\\\10,000 = 7500*(1+0.06/1)^(1*t)\\\\10,000/7500 = (1.06)^(t)\\\\1.33333 \approx (1.06)^(t)\\\\\text{Log}(1.33333) \approx \text{Log}\left((1.06)^(t)\right)\\\\\text{Log}(1.33333) \approx t*\text{Log}(1.06)\\\\t \approx \frac{\text{Log}(1.33333)}{\text{Log}(1.06)}\\\\t \approx 4.937`

The first equation shown is the compound interest formula. I'm assuming that the bank is compounding annually (which means n = 1).

Whenever we have an exponent we want to solve for, we'll involve logs. A good phrase to remember is "If the exponent is in the trees, then log it down".

It takes approximately t = 4.937 years for the £7500 to become £10,000.

Round up to the nearest year to get t = 5 so we ensure that Brian has more than £10,000.