Sinking fund payment a company establishes a sinking fund to...

Sinking Fund Payment: A company establishes a sinking fund to provide for the payment of a $100,000 debt maturing in 4 years. Contributions to the fund are to be made each year. Find the amount of each annual deposit if interest is 3% per annum. Prepare a table showing the annual growth of the sinking fund. (Show all work)

Transcript

0:00 Hi.

00:01 Here, to generate a sinking fund of $100 ,000, we have to find the amount to be deposited annually.

00:14 Here, the time period is four years.

00:21 The rate of interest per year is 0 .03.

00:27 That is 3 person, so 0 .03.

00:29 Number of times the interest is evaluated that is given by n and it is equal to 1.

00:36 Now if a is the amount sinking fund and if p is the amount that has to be deposited every year then we have p into 1 plus r by n into to the part t n minus 1 divided by r by n and this simply we have 100 ,000 to be equal to p into 1 .03 to the power 4 minus 1 upon 0 .03.

01:21 Which implies p is equal to 100 ,000 into 0 .03 divided by 1 .03 to 1 .03 to 1 .03 to the power 4 minus 1 .03 to the power 4 minus 1.

01:43 1 and when we evaluate this this turns out to be equal to $23902 .7.

02:03 Now the growth table is as follows.

02:09 So in the growth table will have four columns.

02:13 One is a payment number, the amount that is deposited annually, the interest incurred and the balance so initially it is zero zero zero and zero first year the amount will be 23, nine hundred and two point seven so initially we won't have any interest and therefore the balance is 23 ,9002 .7 now in the second year again we'll deposit the amount of 23 ,902 .7.

03:06 Now interest will be incurred in this balance and so that is evaluated by 23 ,902 .7.

03:16 That is a balance amount of the previous year into 0 .03 because 3 % is a interest and this turns out to be equal to 717 .08...

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