What will be the compound interest on a sum of Rs 6000 for 2 years at the rate of 10 per annum?

What will be the compound interest on a sum of Rs 6000 for 2 years at the rate of 10 per annum?

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ML Aggarwal Solutions Class 8 Mathematics Solutions for Simple and Compound Interest Exercise 8.2 in Chapter 8 - Simple and Compound Interest

Question 1 Simple and Compound Interest Exercise 8.2

Calculate the compound interest on Rs 6000 at 10% per annum for two years.

Answer:

Given

Rate of interest = 10% per annum

Principal for the first year = Rs 6000

Interest for the first year = Rs (6000 × 10 × 1) / 100

= Rs 600

Amount at the end of first year = Rs 6000 + Rs 600

= Rs 6600

Principal for the second year = Rs 6600

Interest for the second year = Rs (6600 × 10 × 1) / 100

= Rs 660

Amount for the second year = Rs 6600 + Rs 660

= Rs 7260

Therefore, compound interest for 2 years = final amount – (original) Principal

= Rs 7260 – Rs 6000

We get,

= Rs 1260

Video transcript

"hello everybody welcome to lido learning channel my name is rajna chaudhary and we have to solve the question we have to calculate the compound interest on rupees 6000 at 10 per annum for two years so we are given that rate is 10 percent principal is rupees 6000 and time is 2 years so compound interest is interest over interest so we calculate it annually so we will calculate the interest for first year then we will use we will use that amount to calculate interest for the next year so let's find out so interest for first year would be equal to principal into rate into time upon 100 so 6000 multiplied by 10 multiplied by 1 so we have put time as 1 because we are calculating it annually so upon 100 and after further calculation we have 600 now amount for the first year is principal plus interest that means 6000 plus 600 that is 66 double zero now we will use this amount as the interest for the next year because uh next year because that is the compound interest that next interest is charged on the first year's amount so in this case for second year for second year our principal is six six double zero uh rate is ten percent and time is one year now let's find out interest so p into r into t upon hundred the same way same formula let's put the values so we have here 660 as the interest now let's find out amount amount is principal plus interest so principal is six six double zero and interest is six six zero so after adding we would have seven two six zero so this is the amount she has to pay but we do have to find the compound interest so the compound interest would be equal to amount minus principle so this is the final amount 7 2 6 0 and the original principle so original principle that means that she has taken as a principle so after the subtraction we would have rupees one two six zero so this is the final compound address that she has to pay after two years so this is all for the video i hope you understand see you in my next video don't forget to like share and subscribe the channel thank you for watching "

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Compound Interest: The future value (FV) of an investment of present value (PV) dollars earning interest at an annual rate of r compounded m times per year for a period of t years is:

Nội dung chính

  • What Is the Monthly Compound Interest Formula?
  • Monthly Compound Interest Formula
  • Derivation of Monthly Compound Interest Formula
  • Examples Using Monthly Compound Interest Formula
  • FAQs on Monthly Compound Interest Formula
  • What Is the Monthly Compound Interest Formula in Math?
  • How to Calculate Amount Using Monthly Compound Interest Formula?
  • What Is r In the Monthly Compound Interest Formula?
  • What Are the Components of the Monthly Compound Interest Formula?
  • What will be the compound interest on a sum of Rs 6000 /
  • What will be the compound interest on sum of 6000 for 2 years at the rate of 10% per annum?
  • What is the compound interest on a sum of Rs 62500 for 2 years at 12% pa if the interest is compounded 8 monthly?
  • What is the compound interest on Rs 6000 in 2 years?

FV = PV(1 + r/m)mtor

FV = PV(1 + i)n

where i = r/m is the interest per compounding period and n = mt is the number of compounding periods.

One may solve for the present value PV to obtain:

PV = FV/(1 + r/m)mt

Numerical Example: For 4-year investment of $20,000 earning 8.5% per year, with interest re-invested each month, the future value is

FV = PV(1 + r/m)mt   = 20,000(1 + 0.085/12)(12)(4)   = $28,065.30

Notice that the interest earned is $28,065.30 - $20,000 = $8,065.30 -- considerably more than the corresponding simple interest.

Effective Interest Rate: If money is invested at an annual rate r, compounded m times per year, the effective interest rate is:

reff = (1 + r/m)m - 1.

This is the interest rate that would give the same yield if compounded only once per year. In this context r is also called the nominal rate, and is often denoted as rnom.

Numerical Example: A CD paying 9.8% compounded monthly has a nominal rate of rnom = 0.098, and an effective rate of:

r eff =(1 + rnom /m)m   =   (1 + 0.098/12)12 - 1   =  0.1025.

Thus, we get an effective interest rate of 10.25%, since the compounding makes the CD paying 9.8% compounded monthly really pay 10.25% interest over the course of the year.

Mortgage Payments Components: Let where P = principal, r = interest rate per period, n = number of periods, k = number of payments, R = monthly payment, and D = debt balance after K payments, then

R = P r / [1 - (1 + r)-n]

and

D = P (1 + r)k - R [(1 + r)k - 1)/r]

Accelerating Mortgage Payments Components: Suppose one decides to pay more than the monthly payment, the question is how many months will it take until the mortgage is paid off? The answer is, the rounded-up, where:

n = log[x / (x � P r)] / log (1 + r)

where Log is the logarithm in any base, say 10, or e.

Future Value (FV) of an Annuity Components: Ler where R = payment, r = rate of interest, and n = number of payments, then

FV = [ R(1 + r)n - 1 ] / r

Future Value for an Increasing Annuity: It is an increasing annuity is an investment that is earning interest, and into which regular payments of a fixed amount are made. Suppose one makes a payment of R at the end of each compounding period into an investment with a present value of PV, paying interest at an annual rate of r compounded m times per year, then the future value after t years will be

FV = PV(1 + i)n + [ R ( (1 + i)n - 1 ) ] / i where i = r/m is the interest paid each period and n = m t is the total number of periods.

Numerical Example: You deposit $100 per month into an account that now contains $5,000 and earns 5% interest per year compounded monthly. After 10 years, the amount of money in the account is:

FV = PV(1 + i)n + [ R(1 + i)n - 1 ] / i =
5,000(1+0.05/12)120 + [100(1+0.05/12)120 - 1 ] / (0.05/12) = $23,763.28

Value of a Bond:

V is the sum of the value of the dividends and the final payment.

You may like to perform some sensitivity analysis for the "what-if" scenarios by entering different numerical value(s), to make your "good" strategic decision.

Replace the existing numerical example, with your own case-information, and then click one the Calculate.

The monthly compound interest formula is used to find the compound interest per month. Compound interest is widely known as interest on interest. Compound interest for the first period is similar to the simple interest but the difference occurs in and from the second period of time. From the second period, the interest is also calculated on the interest thus earned on the previous period of time, that is why it is known as interest on interest. Let us learn more about the monthly compound interest formula along with solved examples.

What Is the Monthly Compound Interest Formula?

The monthly compound interest formula is also known as the formula of interest on interest calculated per month, the interest is added back to the principal each month. Total compound interest is the final amount excluding the principal amount. 

Monthly Compound Interest Formula

The formula for the compound interest is derived from the difference between the final amount and the principal, which is: CI = Amount - Principal. The formula of monthly compound interest is:

CI = P(1 + (r/12) )12t - P

Where,

  • P is the principal amount,
  • r is the interest rate in decimal form,
  • t is the time.

Derivation of Monthly Compound Interest Formula

The formula for calculating the compound interest is as,

CI = P (1 + r/100)n

  • P is the principal amount
  • r is the rate of interest
  • n is frequency or no. of  times the interest is compounded annually
  • t is the overall tenure.

If the time period for the calculation of interest is monthly, the interest is calculated for each month, and the amount is compounded 12 times a year as there are 12 months in a year. The formula to calculate the compound interest when the principal is compounded monthly is given as: 

 CI = P(1 + (r/12) )12t - P

Here the compound interest is calculated for a month (time period). Thus, the rate of interest r, is divided by 12 and the time period is 12 times.

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Examples Using Monthly Compound Interest Formula

Example1: If Sam lends $1,500 to his friend at an annual interest rate of 4.3%, compounded per month. Calculate the interest after the end of the year by using the compound interest formula.

Solution:  

To find: Compound interest accumulated after 1 year.

P = 1500, r = 0.043 (4.3%), n = 12 , and t = 1 (given)

Using monthly compound interest formula,

CI = P(1 + (r/n) )nt - P

Put the values,

CI = 1500(1 + (0.043/12))12 - 1500

CI = 65.786

Answer: The compound interest after 1 year will be $65.786.

Example 2: James borrowed $600 from the bank at some rate compounded per month and that amount becomes quadruple in 2 years. Calculate the rate at which James borrowed the money by using the monthly compound interest formula.

Solution:

To find: Interest rate

P = 600, n = 12, and t = 2, Amount = 2400 (given)

Using formula,

CI = Amount - Principal

Put the values,

CI = 2400 - 600 = 1800

Using monthly compound interest formula,

CI = P(1 + (r/12) )12t - P

 Put the values,

1800 = 600(1+ (r/12))12×2 - 600

4 = (1+ (r/12))24 

r = 71.4 

Answer: The Interest rate on the given amount of money is 71.4%.

Example 3: Calculate the monthly compound interest on the sum of $6000 borrowed at the rate of 10% for 2 years.

Solution:

To find: Monthly compound interest

P=$6000, r=10%, t=2years (given)

CI = P(1 + (r/12) )12t - P

Put the values,

= 6000(1+10/12)12×2 – 6000

= 7322.35 – 6000 = 1322.35

Answer: The monthly compound interest for 2 years is $1322.35 

FAQs on Monthly Compound Interest Formula

What Is the Monthly Compound Interest Formula in Math?

The monthly compound interest formula is used to find the compound interest per month. The formula of monthly compound interest is: CI = P(1 + (r/12) )12t - P where, P is the principal amount, r is the interest rate in decimal form, and t is the time.

How to Calculate Amount Using Monthly Compound Interest Formula?

There is a direct formula for the calculation of monthly compound interest. A = CI = P(1 + (r/12) )12t 

  • Step 1: Here we need to define the principal and the rate of interest at which the compound interest is calculated so check for the values of P, r and t.
  • Step: Put the values in the formula, A = CI = P(1 + (r/12) )12t 

What Is r In the Monthly Compound Interest Formula?

In the monthly compound interest formula, CI = P(1 + (r/12) )12t - P, r refers to the interest rate on the principal.

What Are the Components of the Monthly Compound Interest Formula?

The calculation of monthly compound interest requires us to know the principal, rate of interest, and the time period. 

What will be the compound interest on a sum of Rs 6000 /

Complete step-by-step answer: 6300 which will be the principal value for second year. So, the amount obtained after the two years is Rs. 6678.

What will be the compound interest on sum of 6000 for 2 years at the rate of 10% per annum?

So the compound interest on rs. 6000 at 10% per annum for 2 years will be rs. 1260 (Ans.)

What is the compound interest on a sum of Rs 62500 for 2 years at 12% pa if the interest is compounded 8 monthly?

∴ C.I = A- P=Rs. 83104−Rs. 62500=Rs. 20604.

What is the compound interest on Rs 6000 in 2 years?

Given that Principal = 6000, n = 2 years, r = 10% per annum. = 7260. = 1260. Therefore the compound interest = 1260 rupees.

What is the compound interest on rupees 6000 in 2 years at 10% pa if compounded yearly?

= Rs 1260. Was this answer helpful?

What will be the compound interest on a sum of Rs 6000 /

Complete step-by-step answer: 6300 which will be the principal value for second year. So, the amount obtained after the two years is Rs. 6678.

What will be the compound interest on Rs 600 for 2 years at 10% per annum?

Calculation: Let the principal be P. ∴ The compound interest is Rs. 1456.

What is the compound interest on Rs 6000 in 2 years?

Given that Principal = 6000, n = 2 years, r = 10% per annum. = 7260. = 1260. Therefore the compound interest = 1260 rupees.