$1000 is deposited into an account at time t=0. The nominal interest rate is 8% compounded...

$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.

Solutions

Expert Solution

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

jeff jeffy answered 2 years ago

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