Amortization of a Loan (Time Value of Money)
I'm having trouble with these 3 questions. I can't figure out how much the interest is applied to, because I don't know how much the loan is amortized up until any specific point. This is for a beginner level finance class.
1.) Your firm had received a $2,000,000 loan from its bank. The loan carries an annual interest rate of 6% and is being amortized in equal quarterly payments (payable at the end of each quarter). The loan has a maturity of 10 years. You now want to repay the remaining balance of the loan in full. At this point of time, there are 10 payments left. What is the loan balance you need to pay now?
2.) When Ms. Jones retired, she received a lump sum of $1,200,000 from her pension plan. She then invested it in an annuity account that would pay her an equal amount at the end of each year for the next 25 year, so that the initial capital of $1,200,000 will be totally depleted. The interest rate for this annuity account is 4% per year. Ms. Jones passed away after receiving the 15th annual payment. Her estate lawyer must now determine the amount of money left that will go to Ms. Jones's heirs. What is this amount?
3.) You have just renegotiated the interest rate of your home mortgage loan. The original loan of $500,000 carries an interest rate of 7%, has an original maturity of 15 years, and requires monthly payments (at the end of the month). There are 80 months remaining to repay the loan. The new mortgage has a lower rate of 6% and will still have 80 months left to maturity. The lender requires a $1500 rate modification fee. First estimate the monthly savings if you switch to the new lower interest rate and then the new gain or loss in present value dollars today if you go through with this rate modification deal.
Any help would be greatly appreciated. Thanks in advance.