# Forces of interest

• Sep 1st 2009, 06:33 PM
tbl9301
Forces of interest
Tawny makes a deposit into a bank account that credits interest at a nominal interest rate of 10% per year, compounded semiannually. At the same time, Fabio deposits 1000 into a different bank account, which is credited with simple interest. At the end of 5 years, the forces of interest on the two accounts are equal, and Fabio’s account has accumulated to Z. Determine Z.

Here is what I have ...
For Fabio, the accumulation function would be 1000(1 + 5i) and the force of interest at time t would be i/(1 + 5i)
The force of interest for Tawny would be ln(1 + i) = ln(1.1) for all t
So I think you set i/(1 + 5i) = ln(1.1) , which would give i = .1821
Then Fabio's account would equal 1000(1 + 5*.1821) = 1910.5 at 5 years
But our teacher said the answer is 1953 so I'm a little off somewhere and can't figure out where. Any help would be great thanks!
• Sep 1st 2009, 07:17 PM
Robb
You forgot to factor in that the nominal interest is compounded semi-annually. If you make this conversion, you get the answer your teacher provided;
so the force of interst for twany should have been $\displaystyle ln(1.1025)=0.09758$ once you take into account the semi-annual compounding.

This gives $\displaystyle i=0.19055$; $\displaystyle 1000\cdot (1+5\cdot 0.19055)=1952.749$