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Hello everyone.
00:01
So this is the question that we have part a company borrowed.
00:07
So principal company borrowed the amount of $60 ,000 for renovation.
00:16
So they plan to they plan to set up a sinking fund that will pay back the loan at the end of five years.
00:27
So time is equal to five years and rate of interest is given in the question rate of interest is equal to 10 % compounded semi -annually.
00:47
So we need to find the sinking fund that is the amount.
00:54
That is amount.
00:57
Part b of the question is abdullah decided to invest.
01:01
So principle amount of investment is equal to thousand dollars quarterly or totally.
01:12
Time for time period which is equal to six years in an ordinary ordinary interest rate so interest rate is equal to 12 percent so i need to tell the amount at the end of six years part c of the question is that we are investing an amount of principal of increase four thousand five hundred dollars for ten years for a time frame of 10 years which is compounded at the rate of interest rate of interest 8 % quarterly so when all withdraws will be made at the end of each period so we need to tell the amount withdrawal with each period so let's jump on to the solution of the question so part a first part a we have a principle the principal amount, so principle, just denote for all the questions, principle i'll denote by p, amount i'll denote by a, then rate of interest is going to be our, time is going to be t, and number of duration is going to be, and this is the duration of compounding.
02:51
So for part a, we have all the necessary values.
02:55
So we'll give the amount, a .n, which is my sinking fund, which is my sinking fund, that is going to be given by the formula.
03:08
A .n is equal to amount, multiplied like 1 plus rate of interest, that is r divided by duration to the power n minus n multiplied by.
03:23
The time minus 1 divided by rate of interest divided by the duration.
03:30
So let's plug in the values over here.
03:32
So this implies this is going to be $60 ,000 is equal to amount 1 plus 0 .1 divided by 2 to the par 2 multiplied by 5 minus 1 divided by 0 .0 .1 divided by 2.
03:50
So this is going to be equal to if i solve this.
03:54
Is equal to amount 60 ,000 multiplied by 0 .1 divided by 2 multiplied by 1 plus 0 .1 divided by 2 with the part 10 minus 1...