Given:

9500 personal loan at 4.5% compounded monthly is to be repaid over a four year term by equal monthly payment .

{9500*0.625} / {1-1/+0.625)^48} =229.70 PMT

and they want us to find: How much interest will be paid in the second year of the loan?

Answers on the text book:

total interest paid in year 2=12 (PMT)- Total principal paid in year 2

total prinical paid in year 2=Balance after year 1 - balance after year 2

=(Balance after 12 payment)-(Balance after 24 payment)

okay here I am having trouble with it why did they use 12 and 24 can someone please explain that to me ?

I do not know where you are getting some of the numbers you use.

Also, you are not using the correct numbers in the formula.

<----------------------------------------------------------------->

What is the periodic payment required to retire a debt of P dollars in n periods (months or years) if payments start at the end of the first period and bear I% interest compounded periodically? For this typical loan payment calculation,

..............R = Pi/[1 - (1 +i)^(-n)]

where R = the rent (periodic payment), P = the amount borrowed, n = the number of payment periods, and i = I/100n.

Example: What is the annual payment required to retire a loan of $10,000 over a period of 5 years at an annual interest rate of 8%? Here, P = 10,000, n = 5, and i = .08 resulting in

......R = 10000(.08)/[1 - (1.08)^-5] = $2504.56 per year

Had the question been what is the monthly payment required to retire a loan of $10,000 over a period of 5 years at an annual interest rate of 8%, compounded monthly? Here, P = 10,000, n = 60, and i = .006666 resulting in

..........R = 10000(.006666)/[1 - (1.006666)^-5] = $202.76 per month or $71.44 less than making yearly payments.

In your case, Given:

$9500 personal loan at 4.5% compounded monthly is to be repaid over a four year term by equal monthly payment .

Here, P = 9500, n = 4(12) = 48 and i = 4.5/100(48) = .00375.

Therefore, R = 9500(.00375)/[1 - (1+.00375)^(-48)]

...............9500(.00375)/[1 - 1/1.19681)]

...............9500(.00375)/.1644485 = $216.63 per month.

As Denis suggested, make a table of the monthly outlays and balances from which you can determine the annual outlays and balances. For instance:

End.of..Starting...Month End...Monthly..Toward....Final

Month...Balance....Interest....Payment...Debt....Balance

.1.......9500.......35.62......216.63....181.....9318.99

.2.....9318.99......34.94......216.63...181.68...9137.30

.3.....9137.30......34.26......216.63...182.36...8954.93

.4.....8954.93......33.58......216.63...183.00...8771.88

.5.....8771.88......32.89......216.63...183.73...8588.14

.6.....8588.14......32.70......216.63...184.42...8403.72

.7.....8403.72......31.511.....216.63...185.11...8218.60

.8.....8218.60......30.82......216.63...185.81...8033.39

.9.....8033.39......30.12......216.63...186.50...7846.89

10.....7846.89......29.42......216.63...187.20...7659.68

11.....7659.68......28.72......216.63...187.91...7471.77

12.....7471.77......28.02......216.63...188.61...7283.16

1 represents month 1

The starting balance is $9500

The end of month interest due is .00375(9500) = $35.62

The monthly payment is $216.63

$216.63 - $35.62 = $181.1 which goes toward reducing the balance.

The end of month 1 balance is therefore $9318.99.

2 represents month 2

The starting balance is $9318.99

The end of month interest due is .00375(9318.99) = $34.94

#216.63 - $34.94 = $181.68

The end of month 2 balance is therefore $9137.30

As you can see from the table, at the end of month 12, only 23.33% of the loan has been repaid.

You can continue to fill in the chart to find the sum of yearly interest for any year you wish. I know of no formula that willl give you the individual yearly sums of interest, debt reduction, etc. If I run across some, I will let you know.