00:01
In this question, we are given that a loan of 36 ,550 is compounded at the interest of 5 % semi -annually and it needs to be repaid with the payments at the end of every six month and the loan was settled in the time period of five years.
00:18
So since it is compounded semi -annually, the payment period is going to be 10 semi -annuals.
00:26
And the interest rate, semi -annual interest rate, is going to be.
00:35
The half of it which will be 5 divided by 2 equals to 2 .5 % now for the first part of the question we have to calculate the size of the periodic payments so for periodic payments we will use the formula it is equivalent to loan amount divided by a present factor this present since we have the value of loan amount this value of present factor will be calculated using the formula 1 minus 1 plus rate of interest r raised to the power minus in divided by r putting in the values we will have 1 minus 1 plus since the rate of interest is 2 .5 it will be 0 .025 raise to the power time period which is minus 10 divided by 0 .025.
01:44
Solving this we will get approximate value to be 8 .752.
01:54
So this will be the value of present factor.
01:56
So finally, therefore, the value of periodic payments is going to be loan amount which is 36 ,500.
02:12
Divided by present factor which is 8 .752...