A company borrows $120000, which will be paid back to the lender in one payment
ID: 2740989 • Letter: A
Question
A company borrows $120000, which will be paid back to the lender in one payment at the end of 9 years. The company agrees to pay semi-annually interest payments at the nominal annual rate of 10% compounded semi-annually. At the same time the company sets up a sinking fund in order to repay the loan at the end of 9 years. The sinking fund pays interest at an annual nominal interest rate of 6% compounded semi-annually. Find the total amount of the semi-annually payments, that is, the sum of the interest payment and the sinking fund payment.
Total semi-annually payment = $__________
Explanation / Answer
Calculate the total semi annually payments:
Number of
payments
Semi -annual
interest
payment
Sinking
fund
Cumulative
sinking fund
Interest
on sinking fund @6%
1
$ 6,000
$ 6,667
$ 6,667
$ 200
2
$ 6,000
$ 6,667
$ 13,334
$ 400
3
$ 6,000
$ 6,667
$ 20,001
$ 600
4
$ 6,000
$ 6,667
$ 26,668
$ 800
5
$ 6,000
$ 6,667
$ 33,335
$ 1,000
6
$ 6,000
$ 6,667
$ 40,002
$ 1,200
7
$ 6,000
$ 6,667
$ 46,669
$ 1,400
8
$ 6,000
$ 6,667
$ 53,336
$ 1,600
9
$ 6,000
$ 6,667
$ 60,003
$ 1,800
10
$ 6,000
$ 6,667
$ 66,670
$ 2,000
11
$ 6,000
$ 6,667
$ 73,337
$ 2,200
12
$ 6,000
$ 6,667
$ 80,004
$ 2,400
13
$ 6,000
$ 6,666
$ 86,670
$ 2,600
14
$ 6,000
$ 6,666
$ 93,336
$ 2,800
15
$ 6,000
$ 6,666
$ 100,002
$ 3,000
16
$ 6,000
$ 6,666
$ 106,668
$ 3,200
17
$ 6,000
$ 6,666
$ 113,334
$ 3,400
18
$ 6,000
$ 6,666
$ 120,000
$ 3,600
$ 108,000
$ 34,201
Total interest paid = $108,000
Total interest on sinking fund = $34,201
Number of
payments
Semi -annual
interest
payment
Sinking
fund
Cumulative
sinking fund
Interest
on sinking fund @6%
1
$ 6,000
$ 6,667
$ 6,667
$ 200
2
$ 6,000
$ 6,667
$ 13,334
$ 400
3
$ 6,000
$ 6,667
$ 20,001
$ 600
4
$ 6,000
$ 6,667
$ 26,668
$ 800
5
$ 6,000
$ 6,667
$ 33,335
$ 1,000
6
$ 6,000
$ 6,667
$ 40,002
$ 1,200
7
$ 6,000
$ 6,667
$ 46,669
$ 1,400
8
$ 6,000
$ 6,667
$ 53,336
$ 1,600
9
$ 6,000
$ 6,667
$ 60,003
$ 1,800
10
$ 6,000
$ 6,667
$ 66,670
$ 2,000
11
$ 6,000
$ 6,667
$ 73,337
$ 2,200
12
$ 6,000
$ 6,667
$ 80,004
$ 2,400
13
$ 6,000
$ 6,666
$ 86,670
$ 2,600
14
$ 6,000
$ 6,666
$ 93,336
$ 2,800
15
$ 6,000
$ 6,666
$ 100,002
$ 3,000
16
$ 6,000
$ 6,666
$ 106,668
$ 3,200
17
$ 6,000
$ 6,666
$ 113,334
$ 3,400
18
$ 6,000
$ 6,666
$ 120,000
$ 3,600
$ 108,000
$ 34,201
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