Nathaniel bought a house for $500,000 ten years ago. He put…

Nathaniel bought a house for $500,000 ten years ago. He put 20% down and financed the balance with a 15-year real estate mortgage at 3%, convertible monthly. Nathaniel decides to pay the remaining loan balance in full by a single payment together with the installment just due. Find the prepayment penalty, which is one-fourth of the lender’s interest loss.

Sam agrees to pay an amount of 2X at the end of 4 years and…

Sam agrees to pay an amount of 2X at the end of 4 years and an amount of X at the end of 7 years. In return, she will receive $5,000 at the end of 6 years and $8,000 at the end of 10 years. At an effective annual interest rate of 3%, find the amount of Sam’s second deposit X.