SOLUTION: Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences ma

Question 1118851: Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
Assume that you take out a $4000 loan for 30 months at 7% APR. How much of the first month's payment is interest? (Round your answer to the nearest cent.)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the loan is 4000 for 30 months at 7% apr.

the payment required per month would be 145.727629 per month.

the first payment is at the end of the first month.

the remaining balance at the beginning of the first month is 4000.

at the end of the first month, the interest is .07/12 * 4000 = 23.333333333.

the payment of 145.727629 is then made.

the principal part of the payment is 145.727629 - 23.3333333 = 122.3942957.

the remaining balance at the end of the first month is 4000 - 122.3942957 = 3877.605704.

as the number of months progress, the interest part is less and less and the principal part is more and more.

this can be seen in the following excel spreadsheet printout.

$$$

i used the TI-BA-II financial calculator to determine what the monthly payment needed to be.

i entered:

present value = 4000
future value = 0
payment is made at the end of the time period.
interest rate per time period is 7/12 = .58333333333.....
number of time periods = 30

i then had the calculator tell me what the required payment was.

the calculator said the required payment was 145.727629 at the end of each month.

you can see from the excel printout that the remaining balance at the end of the 30 month loan period is 0, as it should be.

RELATED QUESTIONS
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can... (answered by CPhill)

Rounding in the calculation of monthly interest rates is discouraged. Such rounding can... (answered by solver91311)

Rounding to the nearest hundredth, 5 is 31.25% of... (answered by brysca)

A 4-metre long pipe is cut into 2 pieces. One piece is five times the length of the other (answered by stanbon)

You are borrowing $7400 to buy a car. If you pay the loan off in 3 years (36 months),... (answered by Boreal)

Why is rounding to the nearest tenth a... (answered by stanbon,richard1234)

can you please show me and explain EACH step in setting up and solving the following... (answered by Earlsdon)

Rounding 38.4687 to the nearest hundredth... (answered by funmath)

Two friends say ‘goodbye’ as they leave the school heading home in different... (answered by math_tutor2020)