Calculating the compound interest with the growing principal is given in detail in the following article. Suppose that some amount of interest is pending to the moneylender at the end of the period maybe it is after a year, half-an-year, quarterly, etc. The interest amount is added to the borrowed sum and that amount becomes the principal amount for the further period of borrowing, This procedure continues until a specific time is found.
Check the step-by-step procedure to solve the compound interest with growing principal problems on the 10th Grade Math Compound Interest article. Compound interest helps to grow your wealth faster. It works as an advantage when comes to investments and will be a potent factor in creating wealth. It helps in increasing inflation, cost of living, and reducing purchasing power.
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What is Compound Interest with Growing Principal?
Suppose that some amount of interest is pending to the moneylender at the end of the period maybe it is after a year, half-an-year, quarterly, etc. The interest amount is added to the borrowed sum and that amount becomes the principal amount for the further period of borrowing, This procedure continues until a specific time is found.
Compound interest benefits investors, banks, and depositors who can receive interest from accounts, bonds, loans, etc. Exponential growth is also important in reducing wealth -eroding factors like inflation, cost of living, and reducing purchase power.
How to Calculate Compound Interest with Growing Principal?
There are a few steps to calculate compound interest with the growing principal:
- In the first step, find out the interest of the principal amount.
- To find the final amount for the year-end we use the formula Principal + Interest.
- The final result of the amount will be the principal amount for the next year.
- Again, the interest amount is found as in step 2.
- To find the compound interest of both years, we add interest amounts for both years.
Compound Interest Examples
If the interest is compounded yearly, then the principal amount will not remain constant every year. Also, it is the same in the case of half-yearly compounded. From the below-given examples, we can clearly understand how compound interest is calculated with the growing principal.
Question 1:
A man takes a loan of $ 20,000 at a compound interest rate of 10% per annum.
(i) Find out the amount after 1 year.
(ii) Find out the compound interest for 2 years.
(iii) Find out the amount of money that is required to clear the debt at the end of 2 years.
(iv) Find out the difference between simple interest and compound interest at the same rate for 2 years.
Solution:
Given that, Amount of loan = $ 20,000
Rate of compound interest = 10%
(i) To find out the interest for the first year = 10% of $ 20,000
= $ 2,000
Therefore, the amount after 1st year = Principal + Interest
= $ 20,000 + 2000
= $ 22,000
(ii) For the next year, the new principal amount is $ 22,000
To find out the interest for the next year = 10% of $ 22,000
= $ 2,200
Therefore, the compound interest for both the years = Interest for 1st year + Interest for 2nd year
= $ 2,000 + $ 2,200
= $ 4,200
(iii) The required amount of money = Principal + Compound Interest for 2 years
= $ 20,000 + $ 4,200
= $ 24,200
(iv) The simple interest for 2 years = P * R * T /100
= $20,000 * 10 * 2 /100
= $ 3,780
Therefore, the required difference = $ 4,200 – $ 3,780
= $ 420
Question 2:
At 5% per annum, the difference between compound and simple interest for 2 years on a particular amount of money is Rs. 180. Find the sum amount?
Solution:
Let the sum of the amount = $ x
The interest for the 1st year = 5% of $ x
= 5 /100 * x
= 5x / 100
= $ x/20
Therefore, the amount after an year = Principal + Interest
= $ x + $ x/20
= $ 21x / 20
For the next year, the new principal is $ 21x / 20
Therefore, the interest for the next year = 5% of $ 21x / 20
= 5/100 * 21x/20
= 110x / 100
At 5% rate simple interest for 2 years = $ 110x / 100 * 5 * T /100
= $ x * 5 * 2 /100
= $ 10x / 100
= $ x /10
Now, according to the problem, we get
110x / 100 – x / 10 = 180
x(110/100 – 1/10) = 180
x / 100 = 180
x = 18000
The required sum of money is $ 18000
Question 3:
Find the compound interest and amount on $20,000 at 10% per annum and in 1 year, interest will be compounded half-yearly.
Solution:
For first half-year principal = $20,000
Rate = 10%
Time = ½ year
The interest for the first half- year = P * R * T / 100
= 20,000 * 10 * 1 / 100 * 2
= $ 1000
Therefore, the amount for the half-year = Principal + Interest
= $20,000 + $ 1000
= $ 21,000
Therefore, at 10% rate the interest for the 2nd half-year = $ 21,000 * 10 * 1 / 100 * 2
= $ 1050
The required sum of money = Principal + Compound Interest
= 21,000 + $ 1050
= $ 22,050
Therefore, the required amount = $ 22,050
Compound Interest = Amount – Principal
= $ 22,050 – $ 20,000
= $ 2,050
Therefore, the Compound Interest is $ 2,050.
FAQs on How do you Calculate Compound Interest when Adding Principal
1. What is the magic of compound interest with the growing principal?
The magic of compound interest with the growing principle is that the amount obtained by adding it to some borrowed amount becomes the principal to the next period. The process continues till the specified time amount is found.
2. What is the principal when interest is compounded yearly?
Whenever the interest is compounded yearly, the principal amount does not remain constant every year.
3. How to calculate compound interest with the growing principal?
Compound interest happens when interest is added to the principal amount borrowed or invested, and again the interest rate is applied to the new principal. It is basically the interest on the interest that leads to exponential growth.
4. What is the principal when interest is compounded half-yearly?
Whenever the interest is compounded half-yearly, the principal amount does not remain constant every half-year, i.e., 6 months.