You deposit 500 pounds at time t=0. At t=5 years, you have 800 pounds. The amount of money you have in the bank can be modeled as V(t)=A*(1+r)^t, where r is the interest rate. Find A and the interest rate r. After how many years will you have 1200 pounds.
At t=0, you deposit 500 pounds in the bank account: V(0)=500=A. At t=5, that amount of money is now, V(5)=800=500*(1+r)^5 i.e. 1+r = 1.6^(1/5) = 1.0986 (4dp) So the interest rate r is 9.86% (3 s.f.)Let T be the time when you have 1200 pounds in the bank. V(T)=500*1.10^T=1200=> T= log(2.4)/log(1.0986)= 9.3 (2 s.f.)If your bank applies the interest annually, you will surpass 1200 pounds in 10 years.
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