Question

Danny owes Patsy 3000 due 10 months from now, and 25 000 due 32 months from now. Danny ask Patsy if he can discharge his obligations by equal payments: one now and the other one 28 months from now. Patsy agrees on condition that a 14,75% interest rate, compounded every two months is applicable. The amount that Danny will pay Patsy 28 months from now will equal approximately 1) 11 455 2) 11 511 3)11 907 4)14 000 5) 20 000

Answer 1

14.75% per annum is 14.75/6=2.4583% every 2 months. The compounding factor is 1.0245833. Danny is going to pay off his debts in two equal payments P, one immediate payment and the other after 28 months. His lower debt is only 3000, so his immediate payment could include this amount, and this debt would be discharged. The remainder  of the first payment, P-3000 plus the second payment=2P-3000 must equal the accumulated amount on the other debt over 28 months=25000*1.0245833^14 (14 2-month periods). This comes to 35123.843. So P=38123.843/2=19061.92, which is approximately 20000, the amount Danny gives Patsy in 28 months' time. (Answer 5). It's clear that the amount paid immediately (which is the same) easily covers the lower debt of 3000.