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Nate purchases an annuity-immediate that pays $400 per month for two years. Nate spends the first four payments and deposits the remaining payments into a savings account that pays an interest rate of 3% compounded monthly. No other deposits or withdrawals are made to the account. (a) Give a single term expression for the actual amount of money in Nate's savings account one year after the purchase of the annuity. (b) What is the balance in the savings account one year after Nate's final deposit? (c) One year after the final deposit, Nate withdraws $5,000 from the account and loans the money to a start-up company. The company agrees to repay the loan with a single payment of $11,000 at the end of 4 years. Assuming the company is able to repay the loan, what is the annual effective interest rate Nate earns on this investment? Nate purchases an annuity-immediate that pays $400 per month for two years. Nate spends the first four payments and deposits the remaining payments into a savings account that pays an interest rate of 3% compounded monthly. No other deposits or withdrawals are made to the account. (a) Give a single term expression for the actual amount of money in Nate's savings account one year after the purchase of the annuity. (b) What is the balance in the savings account one year after Nate's final deposit? (c) One year after the final deposit, Nate withdraws $5,000 from the account and loans the money to a start-up company. The company agrees to repay the loan with a single payment of $11,000 at the end of 4 years. Assuming the company is able to repay the loan, what is the annual effective interest rate Nate earns on this investment