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.
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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.