In: Finance
$1000 is deposited into an account at time t=0. The nominal interest rate is 8% compounded semiannually during the first year. An additional $118.40 is deposited into the account at time t=1 and the fund grows at a force of interest 100 2 t t during the second year.
1) Calculate the semiannual effective interest rate during the first year.
2) Calculate the account value at time t=1 before the additional $118.40 deposit.
3) Calculate the total account value at time t=2.
1) Effective(annual)Interest rate=(1+r/m)^m−1
=(1+.08/2)^2-1
=8.16%
Effective interest rate semi annually =(1+i)^t−1
=(1.0816)^1/2-1
=4%
2)Account value at time t=1 before the addition=Present value(1+i/n)^n
=1000(1+.08/2)^2
=1081.6
3) force of interest rate not clear