1. Ernie makes deposits of 200 at time 0, and X at time 4 . The fund grows at a force of interest delta_t= t/200, for t > 0. The amount of interest earned from time 4 to time 8 is X. Calculate X.
2. Bruce deposits 400 into a bank account. His account is credited interest at a nominal rate of interest of 12% convertible monthly. At the same time, Peter deposits 400 into a separate account. Peter's account is credited interest at a force of interest of delta. After 7.25 years, the value of each account is the same. Calculate delta.
3. Interest on certain deposits is compounded monthly. Find the nominal rate of interest (per annum) for these deposits if the APR is 15%. Obtain the accumulation of an investment of $1,000 over a period of 6 months. How much interest has accrued by that time?