An investment fund has increased in value by a total of 21% over the last 2 years. a)A man invested £1000 in the fund two years ago.What is it worth now? b)Calculate the yearly rate of interest assuming that it was: i)Compound interest ii)Simple Interest working please
+118724 $$P=1000,\quad A=1000*1.21 = 1210\\\\
A = P(1+i)^n\\\\
1210=1000(1+i)^2\\\\
1.21=(1+i)^2\\\\
log1.21=log(1+i)^2\\\\
log1.21=2log(1+i)\\\\
\frac{log1.21}{2}=log(1+i)\\\\
10^{\frac{log1.21}{2}}=10^{log(1+i)}\\\\
10^{\frac{log1.21}{2}}=1+i\\\\
10^{\frac{log1.21}{2}}-1=i\\\\
\:\:i=\:0.1\\\\
\mbox{So the compound annual interest rate is }10\%$$
-------------------------------------------------
SIMPLE INTEREST
I=Prt
2210-1000=1000*r*2
210=1000*r*2
210/2000=r
r=0.105
Simple interest rate it 10.5% per annum
+118724 $$P=1000,\quad A=1000*1.21 = 1210\\\\
A = P(1+i)^n\\\\
1210=1000(1+i)^2\\\\
1.21=(1+i)^2\\\\
log1.21=log(1+i)^2\\\\
log1.21=2log(1+i)\\\\
\frac{log1.21}{2}=log(1+i)\\\\
10^{\frac{log1.21}{2}}=10^{log(1+i)}\\\\
10^{\frac{log1.21}{2}}=1+i\\\\
10^{\frac{log1.21}{2}}-1=i\\\\
\:\:i=\:0.1\\\\
\mbox{So the compound annual interest rate is }10\%$$
-------------------------------------------------
SIMPLE INTEREST
I=Prt
2210-1000=1000*r*2
210=1000*r*2
210/2000=r
r=0.105
Simple interest rate it 10.5% per annum
