 Hello and welcome to the session. In this session we will discuss the following question which says, a limited company impends to create a depreciation fund to replace at the end of the 15th year, as its costing $120,000, calculate the amount to be retained out of profits every year if the interest rate is 7%. Before we move on to the solution, let's discuss the formula to find out the amount of annuity in case of immediate annuity. In case of immediate annuity, the amount of annuity denoted by capital A is equal to small a upon i into 1 plus i to the power of m minus 1 the whole. Where the small a is the annual payment each instalment then the periods annuity percent is the rate of interest and period i is equal to r upon 100. This is the key idea that we use in this question. Let us now proceed with the solution. Now the cost of the assets was $120,000 so this would be the amount of annuity in this case and it's also given that the rate of interest is 7% per annum year so this means it is the case of immediate annuity and so we will use this formula which is what we have in this case given by capital A is $120,000 that is the number of periods of annuity is equal to We can calculate i as r upon 100 equal to 7 upon 100 and so this is equal to 0.07 so we retain out of profits every year. We have to find out small a which is the annual payment of each instalment. Now we use the formula capital A is equal to small a upon i into 1 plus i to the power of n minus 1 the whole. $20,000 is equal to small a upon i which is 0.07 into 1 plus 0.07 which is i to the power of n that is 15 minus 1 the whole. So further we have $120,000 into 0.07 is equal to a into 1.07 to the power of 15 minus 1 the whole. By removing this decimal we have 100 here these to 0 calculate these to 0 and so we have $12,000 into 7 which is $8,500 is equal to a into 1.07 to the power of 15 minus 1 the whole. Let us now find out the value of 1.07 to the power of 15 so this we suppose let x be equal to 1.07 to the power of 15. Now taking log in both sides we have log x is equal to 15 into log of 1.07 further log x is equal to 15 into now the value of log 1.07 is 0.0294 log x is equal to 15 into 0.0294 which is 0.441 this would be equal to 0.441 that means x is equal to 2.761 that is 1.07 to the power of 15 is 2.761. Now putting this value here we have $8,400 is equal to a into 2.761 minus 1 the whole so this gives us $8,400 is equal to a into 1.761 a would be equal to 8,400 upon 1.761 comes out to be equal to first 770.01 and we can say a is equal to $770 approximately. The required amount is equal to $3,770 approximately. Our final answer is this question. Hope you understood the solution of this question.