In how many years will a sum of 12000 becomes $13996.8 at 8 pa rate of compound interest

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:

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• A sum of Rs.12,000 deposited at compound interest doubles after 5 years. After 20 years it will becomeA. Rs. 1,20,000B. Rs. 1,92,000C. Rs. 1,24,000D. Rs. 96,000
• What is the compound interest on a sum of 12000 for 2 years at 8% pa when the interest is compounded annually?
• What is the compound interest on a sum of 12000 at 18% per annum for 1 1 3 years if the interest is compounded 8 monthly?
• What is the compound interest on a sum of 12000 at 18% per annum?
• What will be the compound interest on a sum of 12000?

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]

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)

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.

A sum of Rs.12,000 deposited at compound interest doubles after 5 years. After 20 years it will becomeA. Rs. 1,20,000B. Rs. 1,92,000C. Rs. 1,24,000D. Rs. 96,000

Answer

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Hint: The amount 12,000 doubles which means it becomes $ 2 \times 12,000 = 24,000 $ after 5 years. This means that when the principal amount is Rs.12,000 and the time period is 5 years, the final amount will be Rs. 24,000. So from this we can calculate the interest rate by using the below formula. With the obtained interest rate, the principal amount Rs.12,000 and the time period 20 years, find the final amount at the end of 20th year.
Compound interest A is calculated by $ A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T} $ , where P is the principal amount, T is the time period and R is the interest rate.

Complete step-by-step answer:
We are given that a sum of Rs.12,000 deposited at compound interest doubles after 5 years.
Twice or double of Rs. 12,000 is $ 2 \times 12,000 = Rs.\;24,000 $ .
So here Principal amount P is Rs.12,000, Time period T is 5 years and the final amount A is Rs.24,000.
Interest rate will be,
 $ A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T} $
 $ \Rightarrow 24,000 = 12,000{\left( {1 + \dfrac{R}{{100}}} \right)^5} $
 $ \Rightarrow {\left( {1 + \dfrac{R}{{100}}} \right)^5} = \dfrac{{24,000}}{{12,000}} = 2 $
 $ \Rightarrow \left( {1 + \dfrac{R}{{100}}} \right) = \sqrt[5]{2} \Rightarrow eq\left( 1 \right) $
The above obtained equation is enough to find the amount after 20 years.
Therefore, the total amount after 20 years will be
 $ A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T} $
 $ \Rightarrow A = 12,000{\left( {1 + \dfrac{R}{{100}}} \right)^{20}} $
We already know from equation 1 that $ \left( {1 + \dfrac{R}{{100}}} \right) = \sqrt[5]{2} $ . Substituting this in the above equation, we get
  $ \Rightarrow A = 12,000{\left( {\sqrt[5]{2}} \right)^{20}} $
 $ \Rightarrow A = 12,000{\left[ {{2^{\left( {\dfrac{1}{5}} \right)}}} \right]^{20}} = 12,000 \times {\left( 2 \right)^{\dfrac{1}{5} \times 20}} = 12,000 \times {2^4} $
 $ \therefore A = 12,000 \times 16 = Rs.1,92,000 $
The amount after 20 years will be Rs. 1,92,000.
So, the correct answer is “Rs. 1,92,000”.

Note: The interest can be either simple or compound. In simple interest, the interest amount does not change till the end of the return period whereas in compound interest, the interest amount gradually changes as the interest is imposed on the principal amount plus the previous accumulated interest combined. Compound interest is much greater than Simple interest.

What is the compound interest on a sum of 12000 for 2 years at 8% pa when the interest is compounded annually?

Hence, the compound interest is Rs. 2,520.

What is the compound interest on a sum of 12000 at 18% per annum for 1 1 3 years if the interest is compounded 8 monthly?

2560 will be Rs. 1728 in 4 years. Q2.

What is the compound interest on a sum of 12000 at 18% per annum?

Detailed Solution. Let P = Principal, R = rate % per annum, Time = n years. ∴ Compound Interest is Rs. 1230.

What will be the compound interest on a sum of 12000?

Now Compound interest = A - P ⇒ Compound interest = Rs. 15972 - Rs. 12000 = Rs. 3972.

What is the compound interest on a sum of 12000 for 2 years at 8% pa when the interest is compounded annually nearest to a rupee?

What will be the compound interest on 12000 at the rate of 8% for 1 year the interest being payable half yearly?

How much will 12000 amount to in 2 years at compound interest?

How much will Rs 10000 amount to in 2 years at 10% pa compounded annually?