The problem statement is :
At time 0, John deposits 1000 into a fund which credits interest at a nominal interest rate of 10% compounded semianually. At the same time, he deposits P into a different fund which credits interest at a nominal discount rate of 6% compounded monthly. At time t=20, the amounts in each fund are equal.
What is the annual effective interest rate earned on the total deposits, 1000+P, over the 20 year period?
Solving 1000 (1.05)^40=P (.995)^-240, I get P=2114.
The solutions in the ASM manual says that since the accumulated values of both deposits are the same, I can write (1000+P)(1+i)^20=2000 (1.05)^40. Any insight into why this is the case?
At time 0, John deposits 1000 into a fund which credits interest at a nominal interest rate of 10% compounded semianually. At the same time, he deposits P into a different fund which credits interest at a nominal discount rate of 6% compounded monthly. At time t=20, the amounts in each fund are equal.
What is the annual effective interest rate earned on the total deposits, 1000+P, over the 20 year period?
Solving 1000 (1.05)^40=P (.995)^-240, I get P=2114.
The solutions in the ASM manual says that since the accumulated values of both deposits are the same, I can write (1000+P)(1+i)^20=2000 (1.05)^40. Any insight into why this is the case?
Am I over thinking this? Simple FM Question
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