1) At a certain interest rate the present value of the following two payment patterns are equal:

a) $200 at the end of 5 years plus $500 at the end of 10 years.

b) $400.94 at the end of 5 years.

At the same interest rate of $100 invested now plus $120 invested at the end of 5 years will accumulate to P at the end of 10 years. Find P.

2) An investor makes 3 deposits into a fund, at the end of 1, 3, and 5 years. The amount of the deposit at time t is 100(1.025)^t. Find the size of the fund at the end of 7 years, if the nominal rate of discount convertible quarterly is 4/41.