Let F(t) = Future value at time t, A = Principal = 1000, r = interest rate, m = No. of times compounded annually, t = No. of years
then F(t) = A(1+(r/m))mt
For option 1:
6.2% annual interest rate compounded annually,
F1(t) = A(1+r)t
F1(t) = 1000*1.062t
For option 2:
6.1% annual interest rate, compounded quarterly,
F2(t) = A(1+r/m)mt
F2(t) = 1000(1+(0.061/4))4t
F2(t) = 1000(1.01525)4t
For option 3:
6% annual interest rate, compounded countinously,
Here the formula changes a little bit,
F3(t) = Aert
F3(t) = 1000e0.06t
Now I have graphed them on an app called Desmos on my phone, use y instead of F(t) and x instead of t
Graph in red describes F1(t), the one in green describes F2(t) and the one in purple describes F3(t)
All three converge to (0,1000) and diverge on both sides afterwards.
You can see that F3 > F1 > F2 in the region t<0
You can see that F2> F1>F3 in the region t>0
You can use the third picture to find
Xmin = 20, Xmax = 24
Ymin = 3624, Ymax = 3632
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