(i)When interest is compounded yearly Given: P=Rs10,000; n=18months= year and r=10%p.a. For 1year A=P\left(1+\frac{r}{100}\right)^{n}=10,000\left(1+\frac{10}{100}\right)^{1}=10,000\left(\frac{11}{10}\right)^{1}=\operatorname{Rs} 11,000 For1/2 year P=Rs11,000;n= 1/2 year and r=10% \begin{array}{l} A=P\left(1+\frac{r}{2 \times 100}\right)^{n \times 2}=11,000\left(1+\frac{10}{2 \times 100}\right)^{\frac{1}{2} \times 2}=11,000\left(\frac{21}{20}\right)^{1} \\ =\operatorname{Rs} 11,550 \end{array} C.I.= Rs11,550 - Rs10,000= Rs1,550 (ii)When interest is compounded half-yearly P=Rs10,000; n=1 1/2 year and r=10%p.a. \begin{array}{l} A=P\left(1+\frac{r}{2 \times 100}\right)^{n \times 2}=10,000\left(1+\frac{10}{2 \times 100}\right)^{\frac{3}{2} \times 2} \\ =10,000\left(\frac{21}{20}\right)^{3} \\ =\operatorname{Rs} 11,576.25 \end{array} C.I.= Rs11,576.25 - Rs10,000=Rs1,576.25 Difference between both C.I.= Rs1,576.25 - Rs1,550 = Rs26.25
Saving
The power of compounding grows your savings faster 3 minutes
The sooner you start to save, the more you'll earn with compound interest. Compound interest is the interest you get on:
For example, if you have a savings account, you'll earn interest on your initial savings and on the interest you've already earned. You get interest on your interest. This is different to simple interest. Simple interest is paid only on the principal at the end of the period. A term deposit usually earns simple interest. Save more with compound interestThe power of compounding helps you to save more money. The longer you save, the more interest you earn. So start as soon as you can and save regularly. You'll earn a lot more than if you try to catch up later. For example, if you put $10,000 into a savings account with 3% interest compounded monthly:
Compound interest formulaTo calculate compound interest, use the formula: A = P x (1 + r)n A = ending balanceP = starting balance (or principal)r = interest rate per period as a decimal (for example, 2% becomes 0.02) n = the number of time periods How to calculate compound interestTo calculate how much $2,000 will earn over two years at an interest rate of 5% per year, compounded monthly: 1. Divide the annual interest rate of 5% by 12 (as interest compounds monthly) = 0.0042 2. Calculate the number of time periods (n) in months you'll be earning interest for (2 years x 12 months per year) = 24 3. Use the compound interest formula A = $2,000 x (1+ 0.0042)24A = $2,000 x 1.106 A = $2,211.64
Lorenzo and Sophia compare the compounding effect
Lorenzo and Sophia both decide to invest $10,000 at a 5% interest rate for five years. Sophia earns interest monthly, and Lorenzo earns interest at the end of the five-year term. After five years:
Sophia and Lorenzo both started with the same amount. But Sophia gets $334 more interest than Lorenzo because of the compounding effect. Because Sophia is paid interest each month, the following month she earns interest on interest. Transcript the question is find the difference between the compound interest compounded annually you can see clearly and half yearly question is that find the difference between compound interest compounded yearly and half yearly on rupees 10000 for 18 months at 10% per annum right now let me first ITA awards are given this question it is be having a sum Sum of rupees 10 rupees 10000 so we can write your the principal amount that is we can write a C T is equals to 10000 rupees right and for 18 months that here we can ride the time period 18 months that is we can write 18 months 1 year into one by two Vanya + 1 by two way that is 3 by 2 year we can write 18 months 3 by 2 site and it is also given that at 10% per annum this year it is equals to 10% right now the question is to find difference between compound interest compounded yearly and half yearly Sonal at first find early so we can write for first year as the question is for 18 month this mean for first year and a half year so we can write for 1st year 1st year oral cancer for one year we know that is equal to p into 1 + r100 hold his party nearest is time are is read please principal amount and so we can write SBI m p principal amount is 10000 fittest 10000 INR to 1 + r100 that is we are having Rs 10 sweet is done by hundred party and your first year 1 year so then here we can write it here the value of these tight let me right here here the time period is one year Surya 20 ke cancel bhej dijiye and this will become 10000 INR to US will become 10 plus one that is 11:11 by 10 right and if so then we can see that you did you get cancelled with this hero and we are having amount as 11000 rupees right now as we having a time period of 81 and we are finding money and then as the question is nearly so for nearly here it is for one year and then for half yearly for half year at me it also for happy so we know that if amount is equal to p into 1 + R by hundred hold his party so here as at the end of one year we're having the amount is 11000 so here we can say that here in this here for their a week and I were the principal mounted 11000 11000 into oneplus as we having great as 10% so it is done by hundred and hold is power half year sweaters have right now multiplier here to see this year we also have to multiply Bittu so here we can write it has 11000 into this 0k cancel with this hero and B having 20 + United 21 by 20 and yards to get cancelled with this two and just hold is 52 now if it's all this then we will get an answer as this is as 11550 height so we can see that here the compound interest when we are calling for yearly compound interest 11550 rupees -10000 which is equals to 1558 Soviet salt for nearly 9 half yearly so let me right here for half yearly for half yearly light show in the TV and B having at at starting the principal amount at 10000 it is 10000 and the time period is here 18 months and we can write 18 months as time is equal to 18 months to 2 years 3 by 2 year and also the rate is given as 10% right so we can write it as the is equal to zero the formula that is equal to p into 1 + r100 hold is to our time that is so if we put here are the values then we can write the principle as 10000 principal amount is 10000 INR to 1 + are here we're having read as 10% sweetest and by 100 whole raise to power it and we are having time is equal to 3 by 2 naahi let multiply with two so he also had to so this will be come here this to get cancelled with this too and we are having 10000 INR to hear this Hero ke cancel with this is also it is to Newton that is 2020 plus two letters 21 by 20 whole cube right now he was all this then we will get here ten thousand ten thousand ine 221 cube / 20 cube is equal to 8000 right now here is the easy Rose get cancelled then you will get an answer here was 11570 6.25 here this is in case when we have when we are finding here in first year and here we are calling for half yearly sweater in half yearly we get our amount is 11570 6.25 right as we neared the compound interest is equals to amount - principal here as we use here that amount here is a amount - principal so as any amount - pixel that is 11576.2 minus the principle that is 10000 rights we were soldiers then we can write here the compound interest here we are having is 1570 6.2 5 rupees right but as the questions is to find the difference between compound interest and half yearly so here we get the compound interest early as 1550 and compound interest half yearly is 1570 6.25 so we can say that difference between difference between both compound interest as Indian half yearly theatres 157 6.25 it is on it is one half yearly - compound interest when it is nearly so it is 1550 so it was all this then we will get the answer is this then it is 26.2 5 rupees hence we can see that it is the difference and and frequency that this of final answer thank you No worries! 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What is the difference between the compound interests on Rs 10000 for 1 1 2 years at 4% per annum compounded yearly and half yearly?
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