Question 286379: A company wants to set up a sinking fund for the repayment of a loan of 100million at the end of four years.It makes equal deposits at the end of each month into a fund that earns interest at 22% per year compounded monthly. Determine the size of each deposit and construct a sinking fund schedule(the first three months only)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Loan is $100 million to be repaid at the end of 4 years.
Monthly deposits are made.
Interest rate is 22% per year compounded monthly.
This is a Payment for a Future Value type problem.
Using a financial calculator, you would enter:
Number of Time periods = 4 * 12 = 48
Interest Rate per Time Period = 22% / 100% = .22 / 12 = .0183333333
Future Amount = $100 million
Payments are made at the end of each month.
You are looking for the payment amount.
Your answer would be (using the financial calculator)"
Payment is $1,317,274.45 per month.
Sinking Fund Balance for the first 3 months would be:
(1+i) = 1.0183333333 per month
p = $1,317,274.45 per month
End of month 1 = $1,317,274.456
End of month 2 = $1,317,274.456 * (1+i) = $1,341,424.482 + p = $2,658,698.932
End of month 3 = $2,658,698.932 * (1+i) = $2,707,441.746 + p = $4,024,716.196
.....
End of month 47 = $96,906,113.47 * (1+i) = $98,682,725.55 + p = $100,000,000.00
If you do not have a financial calculator, you can get an online version that will help you do the same problem.
As a last resort, you can use the formula given in the following lesson on Payment for a Future Value.
PAYMENT FOR A FUTURE VALUE
The equation to use from that lesson is:
PAYMENT FOR A FUTURE VALUE EQUATION
PMT = Payment per Time Period
FV = Future Value
i = Interest Rate per Time Period
n = Number of Time Periods
FV = $100,000,000
i = .22 / 12 = .01833333333
n = 12*4 = 48
Intermediate calculations would be:
(1.01833333333)^48 - 1 = 1.391762614
Equation would become:
PMT = 100,000,000 / (1.391762614/.01833333333) which would become:
PMT = $1,317,274.45
An online financial calculator that will also calculate this for you can be found at the following link:
http://www.arachnoid.com/lutusp/finance.html
You enter the information that you have and you click on the value you are looking for.
For example:
I entered values for:
Future Value.
Interest Rate per time period.
Number of time periods.
Present Value (I set it equal to 0).
I set the payment to be made at the end of the time period.
I then clicked on the button for Payment.
I got the same result that I gave you using both my own financial calculator plus solving the equation from the lesson.
One last item.
All equations used here assume re-investment of the interest earned each month.
That re-investment is assumed to be at the same interest rate used for calculating the payment.
I used Excel to calculate the money accruing in the sinking fund for every time period, not just the first 3.
The results are shown below:
Time Period
Present Value of Loan
Payment
Interest Rate
Sinking Fund Balance
0 $41,810,169.363 0.018333333 $0.000
1 1,317,274.450 $1,317,274.450
2 1,317,274.450 $2,658,698.932
3 1,317,274.450 $4,024,716.196
4 1,317,274.450 $5,415,777.110
5 1,317,274.450 $6,832,340.807
6 1,317,274.450 $8,274,874.839
7 1,317,274.450 $9,743,855.328
8 1,317,274.450 $11,239,767.126
9 1,317,274.450 $12,763,103.974
10 1,317,274.450 $14,314,368.663
11 1,317,274.450 $15,894,073.206
12 1,317,274.450 $17,502,738.998
13 1,317,274.450 $19,140,896.997
14 1,317,274.450 $20,809,087.892
15 1,317,274.450 $22,507,862.287
16 1,317,274.450 $24,237,780.879
17 1,317,274.450 $25,999,414.646
18 1,317,274.450 $27,793,345.031
19 1,317,274.450 $29,620,164.140
20 1,317,274.450 $31,480,474.933
21 1,317,274.450 $33,374,891.424
22 1,317,274.450 $35,304,038.884
23 1,317,274.450 $37,268,554.047
24 1,317,274.450 $39,269,085.321
25 1,317,274.450 $41,306,293.002
26 1,317,274.450 $43,380,849.491
27 1,317,274.450 $45,493,439.515
28 1,317,274.450 $47,644,760.357
29 1,317,274.450 $49,835,522.080
30 1,317,274.450 $52,066,447.769
31 1,317,274.450 $54,338,273.761
32 1,317,274.450 $56,651,749.897
33 1,317,274.450 $59,007,639.762
34 1,317,274.450 $61,406,720.942
35 1,317,274.450 $63,849,785.276
36 1,317,274.450 $66,337,639.123
37 1,317,274.450 $68,871,103.624
38 1,317,274.450 $71,451,014.974
39 1,317,274.450 $74,078,224.699
40 1,317,274.450 $76,753,599.935
41 1,317,274.450 $79,478,023.717
42 1,317,274.450 $82,252,395.269
43 1,317,274.450 $85,077,630.299
44 1,317,274.450 $87,954,661.305
45 1,317,274.450 $90,884,437.879
46 1,317,274.450 $93,867,927.024
47 1,317,274.450 $96,906,113.470
48 1,317,274.450 $100,000,000.000
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