What is the compound interest in RD of Rs 12500 at the rate of 12% per annum compounded yearly for 2 years?

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RD Sharma Solutions Class 8 Mathematics Solutions for Compound Interest Exercise 14.2 in Chapter 14 - Compound Interest

Question 30 Compound Interest Exercise 14.2

Find the amount of Rs. 12500 for 2 years compounded annually, the rate ofinterest being 15% for the first year and 16% for the second year.

Answer:

Given details are,

Principal (p) = Rs 12500

Rate1 (r) = 15% and Rate2 = 16%

Time (t) = 2 years

By using the formula,

A = P (1 + R1/100 × 1 + R2/100)

= 12500 (1 + 15/100 × 1 + 16/100)

= 12500 (1.15 × 1.16)

= Rs 16675

∴ Amount after two years is Rs 16675

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Find the compound interest on Rs. 12500 at $ 8\% $ per annum for 9 months compounded quarterly.A. 1020B. 1428C. 765D. 550

Answer

Verified

Hint: To solve this question, we need to gather information from the question such as principal, rate of interest and time and then to find the compound interest put these values in the formula given as
${\text{total amount}} = {\text{principal amount}} \times {\left( {{\text{1 + }}\dfrac{{{\text{rate}}}}{{100}}} \right)^{{\text{time}}}}$

Complete step-by-step answer:
Given that
Principal amount= Rs. 12500
Rate compounded quarterly
\[ \Rightarrow {\text{rate}} = \dfrac{8}{4} = 2\% \]
Time =9 months
$ = \dfrac{9}{{12}}years = \dfrac{9}{{12}} \times 4{\text{ }}quarters = 3{\text{ }}quaters$
As we know that,
 Compound interest = total amount – principal amount
Total amount is given by
$ \Rightarrow {\text{total amount}} = {\text{principal amount}} \times {\left( {{\text{1 + }}\dfrac{{{\text{rate}}}}{{100}}} \right)^{{\text{time}}}}$
Substituting the values in the above formula, we get
\[
  \Rightarrow {\text{total amount}} = 12500 \times {\left( {1 + \dfrac{2}{{100}}} \right)^3} = 12500 \times {\left( {\dfrac{{51}}{{50}}} \right)^3} \\
   \Rightarrow {\text{total amount}} = {\text{Rs}}{\text{. 13265}} \\
\]

Compound interest = total amount – principal amount
$
   = {\text{Rs}}{\text{. }}\left( {13265 - 12500} \right) \\
   = {\text{Rs}}{\text{. 765}} \\
 $
Hence, compound interest is 765 rupees.

So, the correct answer is “Option C”.

Note: Remember the formula of total amount, when interest is compounded timely. This question is formula based and some values or conditions are given in the questions. You have to find those values from the question and put them directly into the formula. And always try to solve the problems in steps such as the first step: find the given conditions or values and Second, which formula to be used and so on.

What is the calculator about?
The Recurring Deposit (RD) calculator will help you calculate the maturity value of the investment if it grows at a certain interest rate.

How to use it
The maturity value of the deposit will depend on the amount of investment, duration of the deposit and the interest rate.

You will have to enter the date of opening of the FDRD, and then enter the amount of deposit which has to between Rs 500 and Rs 10 lakh. Thereafter, the duration has to be entered in months which have to be between 6 months and 120 months.

Lastly, enter the annual rate of interest at which the recurring deposit investment has been made.

One can use the slider to put in different recurring deposit amounts to arrive at the final maturity value.

What it shows
On submitting the above information, the calculator will show the final maturity value of the investment. Based on the date of deposit and the tenure, the maturity date of the investment will also be shown. In addition, the break-up of maturity value, i.e., the investment amount and the interest earned will be shown separately.

How the result is arrived at
The formula used for arriving at the maturity value of a recurring deposit over a certain period at a certain interest rate is:

In case of recurring deposits, the compounding happens on quarterly basis.

The formula is: A = P*(1+R/N)^(Nt)

Here, A is the maturity amount in Rs., the recurring deposit amount is 'P' in Rs., 'N' is the compounding frequency, interest rate R in percentage and 't' is the tenure.

For a 12 month RD of Rs 5,000 at 8 percent per annum, the maturity value will be the sum of the series as below:

A = P*(1+R/N)^(Nt)
= 5000*(1+.0825/4)^(4*12/12) = 5425.44
= 5000*(1+.0825/4)^(4*11/12) = 5388.64
...
= 5000*(1+.0825/4)^(4*1/12) = 5034.14
Total maturity value ( sum of series) = Rs 62730.85

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