If P1 money is invested @ rate r1 and P2 is invested @r2 rate compounded annually both for the same duration, then what is the weighted avg compound rate for the total money P1+P2?
What is the weighted average rate if it were a case of simple interest?
Solution:
Consider simple interest first of the following amounts:
300@5% and 500@7% for same duration.
What is the weighted average rate if it were a case of simple interest?
Solution:
Consider simple interest first of the following amounts:
300@5% and 500@7% for same duration.
Overall interest per year =3*5+5*7=50. overall Principal =300+500=800
Interest per 100 principal per year =50/8=(3*5+5*7)/8 which is the weighted avg of individual rates.
How does it work for compound interest?
Total Amount after n years
Total Amount after n years
=P1*(1+r1)**n + P2*(1+r2)**n
And this should be equal to
And this should be equal to
=(P1+P2)*(1+r)**n where r is wted avg compound rate
r= [ [P1*(1+r1)**n + P2*(1+r2)**n]/ (P1+P2) ]**(1/n) - 1
In effect meaning that the weights for compound interest are the (1+r)**n factors. Of course one has to apply the inverse root and subtract one finally
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