1a. Kumi Ltd permits its customers to pay with a credit card or to receive a percentage discount x for paying cash. For credit card purchases, the company receives 97% of the purchase price one-half month later. Determine the value of that would make the two payment methods equivalent if the companys annual rate of return is 14%.

b. At time 0, M is deposited into Fund X, which accumulates at a force of interest _t = 0.006t². At time m, 2M is deposited into Fund Y, which accumulates at an annual effective rate of 10%. At time n, where n > m, the accumulated value of each fund is 4M.

Determine m.