00:01
In this problem, we are given the present value of the amount that the merchant borrows from the bank is equivalent to 15 m .i .d.
00:15
He is going to pay back in installment of 10 years where the rate of interest i is equal to 12%.
00:23
Now, we need to find out the amount when the interest is annual.
00:34
So, we can write the semi -annual interest r is equivalent to 1 plus i raised to the power of half minus 1.
00:56
So, which is equivalent to 1 plus 12 divided by 100 raised to the power of half minus 1 which is equivalent to 5 .83%.
01:08
Now, the installment we can find out using the formula present value into the rate of interest divided by 1 minus 1 plus power raised to the power of minus 2t.
01:27
So, let us substitute the value which is equivalent to 15 multiplied by 0 .0583 divided by 1 minus 1 plus 0 .0583 raised to the power of minus 20.
01:48
Hence upon solving, we get the value as equivalent to 1 .2897 m .i .d.
01:56
This is the answer of the first part of the question.
02:02
Next, we have to find out the installment value when the interest is compounded semi -annually.
02:16
So r is equal to i divided by 2 which is equal to 12 by 2 which is equivalent to 6%...