Suppose you borrow P dollars at a monthly interest rate of r (as a decimal) and wish to pay off the loan in t months. Then your monthly payment can be calculated using the following formula in dollars.
\(\displaystyle M = \frac {Pr(1+r)^t}{(1+r)^t-1}\)
Remember that for monthly compounding, you get the monthly rate by dividing the APR by 12. Suppose you borrow $9000 at 9% APR (meaning that you use r = 0.09/12 in the preceding formula) and pay it back in 2 years.
(a) What is your monthly payment? (Round your answer to the nearest cent.)
411.16
(b) Lets look ahead to the time when the loan is paid off. (Round your answers to the nearest cent.)
(i) What is the total amount you paid to the bank?
9867.84
(ii) How much of that was interest?
867.84
(c) The amount B that you still owe the bank after making k monthly payments can be calculated using the variables r, P, and t. The relationship is given by the formula below in dollars.
\(\displaystyle B = P \left( \frac {(1+r)^t-(1+r)^k}{(1+r)^t-1}\right)\)
(i) How much do you still owe the bank after 1 year of payments? (Round your answer to the nearest cent.)
(I'm stuck here. If I put the formula into the calculator, I get answers in the negatives. r = 0.0075 and k = 411.16, right? I'm so confused.)
\(\displaystyle M = \frac {Pr(1+r)^t}{(1+r)^t-1}\)
Remember that for monthly compounding, you get the monthly rate by dividing the APR by 12. Suppose you borrow $9000 at 9% APR (meaning that you use r = 0.09/12 in the preceding formula) and pay it back in 2 years.
(a) What is your monthly payment? (Round your answer to the nearest cent.)
411.16
(b) Lets look ahead to the time when the loan is paid off. (Round your answers to the nearest cent.)
(i) What is the total amount you paid to the bank?
9867.84
(ii) How much of that was interest?
867.84
(c) The amount B that you still owe the bank after making k monthly payments can be calculated using the variables r, P, and t. The relationship is given by the formula below in dollars.
\(\displaystyle B = P \left( \frac {(1+r)^t-(1+r)^k}{(1+r)^t-1}\right)\)
(i) How much do you still owe the bank after 1 year of payments? (Round your answer to the nearest cent.)
(I'm stuck here. If I put the formula into the calculator, I get answers in the negatives. r = 0.0075 and k = 411.16, right? I'm so confused.)
