66. The DeHaven family, tracing lineage back to the American Revolution, claimsthat in Decem- ber 1777 their ancestor Jacob DeHaven loaned George Washington $450,000 in gold and sup- plies which helped turn the tide of the war. Recal that the future value of a loan is VVo (1 0 of initial value Vo invested at annual rate r com pounded n times per year for t years (a) In 1989 (as well as several points during the 19th century), the descendants wished to claim compensation for this princely sum and assumed a 6% interest rate compounded monthly. How much did the family request as the value of the loan? (b) If $100,000, 000 was what the DeHaven family was owed "fairly" after 212 years of 6% interest compounded monthly, what does that assume the original loan value to be? (This is called the present value of the investment) (c) Citing their reasonableness, the descendants claimed that $100,000,000 was a sufficient compensation. What annual interest rate (compounded monthly) does this amount to over the course of the loan's term from 1777 until 1989? (d) In the 1920's (let's say 1925) President Coolidge recommended to Congress that the loan, valued at $4,000,000, should be re paid. What interest rate does that assume? 66. The DeHaven family, tracing lineage back to the American Revolution, claimsthat in Decem- ber 1777 their ancestor Jacob DeHaven loaned George Washington $450,000 in gold and sup- plies which helped turn the tide of the war. Recal that the future value of a loan is VVo (1 0 of initial value Vo invested at annual rate r com pounded n times per year for t years (a) In 1989 (as well as several points during the 19th century), the descendants wished to claim compensation for this princely sum and assumed a 6% interest rate compounded monthly. How much did the family request as the value of the loan? (b) If $100,000, 000 was what the DeHaven family was owed "fairly" after 212 years of 6% interest compounded monthly, what does that assume the original loan value to be? (This is called the present value of the investment) (c) Citing their reasonableness, the descendants claimed that $100,000,000 was a sufficient compensation. What annual interest rate (compounded monthly) does this amount to over the course of the loan's term from 1777 until 1989? (d) In the 1920's (let's say 1925) President Coolidge recommended to Congress that the loan, valued at $4,000,000, should be re paid. What interest rate does that assume