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10 REM "Scholarship Test" 20 INPUT "Enter marks secured", $\begin{array}{ll}\text { S } & \text { 30 }\end{array}$ 40 If $\mathrm{S}>50 \mathrm{AND} \mathrm{S}<60 \mathrm{THEN}$ Let $\quad 50 \mathrm{~S}=\mathrm{S}+1000$ 60 If $S>70$ AND $<80$ THEN Let $\quad 70 \mathrm{~S}=\mathrm{S}+2000$ $80 \quad$ If $S>75$ THEN $S=S+2500$ 90 If $S>80$ THEN $S=S+3000$ 100 If $\mathrm{S}<50$ THEN 110 PRINT "You are not eligible for the Scholarship Test" 120 PRINT "Your Scholarship amount is:" S 100 END If $S=72$, then what is the scholarship that a student gets? (1) $\operatorname{Rs} 2572$ (2) $\operatorname{Rs} 3072$ (3) $\operatorname{Rs} 2072$ (4) Rs 4572

So we have ah, company that is investing $10,000 every three months and they're getting 10.5% interest compounded quarterly, and we want to find how much there will be after 10 years. So after 10 years in this account, and so we know that means that interest is going to be a crude 40 times 40 times there will be getting interest, Um, for that, that first money that they put in. So let's say we look at the money way. Have the money that was originally invested would be this. That's how much money, the very first after 10 years. That's how much money the the original $10,000 would be worth now, three months later, they also put it on money. But it would Onley have been in there instead of for 40 quarters. It would have on Lee been in there for a total of 39 quarters, and then the next time they deposited money. After 10 years, that money hasn't been in there is long it's been in there, and would Onley have received interest 38 times, all the way down to when they get to that last deposit of $10,000 then this money hasn't accrued on the interest yet. So what do we want to do? We want to add up all these terms. I want to add up all these terms. So we want the sum of 40 terms. And we know we have 10,000 times one minus. And I'm going to call this our the constant ratio to the 40th power over one minus the constant ratio. And so I put this into my calculator and stored it, I'd actually started as X and again, that's going right there. And when you type that in for that, some of that Siri's you will get 69 693,000, $30.84. Now they actually put in $10,000 40 different times, so there would be $400,000 of money that they have invested. So how much interest? Not too hard to attract this. So here is the worth after 10 years, and this is the amount of interest they would have earned after 10 years. Pretty darn good at 10.5% a nice interest rate

For part of the question will be using this formula here to find you the value of any weight. So that means we're going to need a value for P I and Mountain. He is the amount of money that we're depositing, Um, every period. So the company is investing 10,000 Ah, at the end of every three months. So that means he is 10,000. Are is the interest rate. So that's 10.5%. People change that to a decimal, so that's going to be 0.10 and as the number of compound periods per year. So the interest rate is compounded quarterly, which means they're going to be four compound and periods per year. Lastly, T is the total number of years. So we're told that the company will be doing this for 10 years. So tea is tough, and now we can put all these valleys into this red formula to find the value of the annuity. So this is going to equal 10,000 time one plus zero only 105 divided by four raising that the power of ward hearts 10. It's attract one and then divide everything by 0.105 So this works out to be 693,000 and 30 hurting $1. Rounding to the nearest dollar, Kate and then Part B were asked to find the interest. So interest is going to be equal to the total value of the annuity. So that's a minus, uh, the total value of principle. So the sum of all the principal deposits that you're putting it so cold some people. So this is going to be equal to 693 031 minus. So we know that each deposit is 10,000 and we're doing that four times per year for a total of 10 years suffering. Subtract this Lord Hutton's 10. You will get that the interest amount is 293 03

According to the question, the water investment that is being made for the scholarship filled the principle, which is equal to 10,000 dollars every three months so n will be equal to four. Why is D is equal to 10 on the rate of interest? Quarterly is equal to 10.5% so it will become 0.10 fight. Now we know that the amount of the annuity is given us principled multiplied with one plus R divided by n raised to the part Off empty, the minus one, divided by R, divided by in supporting the values will get 10,000 multiplied with one plus one 0.105 divided by four. Race to the part off for multiplied that stand minus one, divided by 0.105 divided by four, which will be equal to 693,000 on $30.84 which is approximately equal to 693 on $31. So this was the total amount that every generated for the scholarship After 10 years. Now, the interest paid will be equal to the amount minus the total deposits which will be equal toe 69,003 609 693,031 dollars minus 40 multiplied bit $10,000 which is equal to 29,000 293,000 on $31.

Part of this question. We're asked to find the value of this annuity after 10 years. So which means we're going to be using this formula here. So we're going to need valleys for E are and and he is amount of money that's being deposited in each period. So that's £15. Are is Thea Animal interesting? So, um, we're given that the interest rate is 9% meaning are a 0.0 yeah, on as the number of compounding here is prettier. So since it's compounded quarterly, this means that their validity for comforting periods per year and he is a total number of years. So this is, and now we can solve more develop annuity. You just have to substitute those values into the formula of their in bred the 10,000 times one plus 0.9 divided by four to the power of four times 10 40 the track one, and by that by 0.9 over so best value relates to 956,000 $793 rounded toe years dollars in Part B were asked to find the interest of so interest. Let's call that I is going to be equal to the total amount of annuity. So that a that we found in party minus the total principal put into the so this is going to be equal to 956793 minus. That's 15,000 per quarter, 4/4 per year for a total of 10 years, So this is going to equal $356,793.