What is the interest if rupees 30000 was invested for one year at 40 per annum compounded quarterly?

The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is A. 2 yearsB. \[2\dfrac{1}{2}\] yearsC. 3 yearsD. 4 years

Answer

Hint: We had to only apply the compound interest formula that is \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}\], where A is the amount after n years, P is the principal amount, r is the rate of interest and n is the number of years i.e. time period.

Complete step-by-step answer:
Let the time period be t years.
Now as we know that the compound interest is applied on Rs. 30,000.
So, the principal amount will be = P = Rs. 30,000
Now the amount after t years will be = A = Principal amount + Compound Interest for t years = 30,000 + 4347 = Rs. 34,347.
Now the given compounded rate of interest per annum is = r = 7%.
So, now let us apply compound interest formula.
\[ \Rightarrow 34,347 = 30,000{\left( {1 + \dfrac{7}{{100}}} \right)^t}\]
Dividing both sides of the above equation by 30000.
\[ \Rightarrow \dfrac{{34347}}{{30000}} = {\left( {1 + \dfrac{7}{{100}}} \right)^t}\]
\[ \Rightarrow \dfrac{{11449}}{{10000}} = {\left( {\dfrac{{107}}{{100}}} \right)^t}\]
\[ \Rightarrow {\left( {\dfrac{{107}}{{100}}} \right)^2} = {\left( {\dfrac{{107}}{{100}}} \right)^t}\]
So, comparing powers of both the sides of the above equation.
t = 2 years
So, the time period will be 2 years.
Hence, the correct option will be A.

Note: - Whenever we come up with this type of problem then there is only one method to find the value of any one of the elements (principal amount, final amount, rate of interest, time period). We had to apply compound interest formula and then put all the given values in that. And after solving that equation we will get the required value of that element (here time period in years). This will be the easiest and efficient way to find the solution of the problem.

What is Future Value?

Future value is the utility of cash or an asset at a particular date in the future. It shows you the amount to which a current asset would grow over some time. The future value is a crucial concept as it shows you the value of your current savings in the future. You get an idea of how much an investment today is worth in the future.

The future value is important to both investors and financial planners, as they may estimate how much an investment today is worth in the future. It helps investors make sound financial decisions based on their financial goals.

Understanding the concept of future value helps you to earn a return above inflation. Inflation is the climb in the prices of goods and services over some time. Your investment must beat inflation over the long-term if you want to achieve crucial financial goals, such as buying a car or accumulating a corpus for children’s higher education and marriage.

Future value is significant for a business. If you invest money in a new project, it is essential to know the return on investment. Future value helps you to calculate the potential return from the project.

What is the Future Value Calculator?

The future value calculator is a simulation that calculates the future value of an investment. It shows you what your money is worth in the future. A future value calculator is a smart tool that computes the value of any investment at a specific time in the future.

The future value calculator consists of a formula box, where you enter the initial investment, periodic investment, rate of interest, and the number of periods. The calculator will display the future value of your investment.

How does Future Value Calculators work?

The future value calculator calculates the future value (FV) of an investment for a series of regular deposits, on a set rate of interest (r), and the number of years (t).

You must use the mathematical formula:

A = PMT ((1+r/n)^nt – 1) / (r/n))

(The formula assumes the deposits are made at the end of each period such as month or year).

A = Future Value of the Investment
PMT = Payment amount for each period
n = Number of compounds per period
t = Number of periods the money is invested

For example, you deposit Rs 10,000 per month (The deposit is made at the end of each month) at an interest rate of 8% compounded monthly. (This is 12 compounds per period). You may calculate the value of the investment after 10 years as follows:

PMT = Rs 10,000
n = 12 (Number of compounds per period is 12 for monthly compounding)
t = 10 years

A = (10,000(((1+0.08/12)^(120) – 1) / (0.08/12)))
A = Rs 18,29,460.

You have the mathematical formula if deposits are made at the beginning of each period:

A = PMT (((1 + r/n)^(nt) – 1) / (r/n)) * (1+r/n)

Let’s do the calculation with the same figures as above.

A = 10,000 (((1+0.08/12)^120 -1) / (0.08/12) * (1+0.08/12)

A = 18,17,345

How to use the ClearTax Future Value Calculators?

The ClearTax Future Value Calculator shows you the future value of your investments in seconds. To use the ClearTax Future Value Calculator:

• You must enter the monthly investment.
• Enter the annual interest.
• You then select the compounding as monthly, quarterly, half-yearly, or yearly.
• Enter 0 as the Present Value.
• Select the number of years for the investment.
• You then select PMT as the beginning or end of each compound period.
• The ClearTax Future Value Calculator displays the future value of the investment.

FAQs on the ClearTax Future Value Calculator

• Why does ClearTax Future Value Calculator ask for the period of compounding of the interest rate?

  Compounding is a process where the earnings of the assets are reinvested to earn additional earnings over time. The compounding period is a period when the interest was last compounded and when it will be compounded again.
  Interest may be compounded on any frequency schedule from daily to annually. However, when you calculate compound interest, the period of compounding makes a significant difference.
  For example, the amount of compound interest that accrues on Rs 10,000 compounded at 8% annually for five years, will be lower as compared to Rs 10,000 compounded quarterly, at the same rate of interest over the same period. The ClearTax Future Value Calculator takes the period of compounding into account when calculating the future value of your investment.

• How does the ClearTax Future Value Calculator help me?

  Well, you can calculate the future value of your investments. It helps you to set financial goals such as buying a dream house, doing retirement planning, or investing for a child’s higher education and marriage.
  The ClearTax Future Value Calculator shows you the future value of your investments, depending on the rate of interest and period you select for the requisite investment. You may calculate the future value of investments at different interest rates and over the various periods to select the best investment.

• Is the ClearTax Future Value Calculator easy to use?

  You may use the ClearTax Future Value Calculator from the comfort of your house and calculate the future value of your investments in seconds.

• How does ClearTax Future Value Calculator help your business?

  Businesses would consider the time value of money before investing in a project. They need to know the future value of the investment, as compared to today’s present value. The future earnings help the business decide if the current investment in the project has benefits over the long-term.

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