In this article, you will learn about How to Calculate Compound Interest with Periodic Deductions or Additions to the Amount. Practice the Problems in Periodic Compound Interest and learn how to solve the related problems. To help you understand the concept better we even listed the Formula along with Step by Step Solutions. Check out the Solved Examples for finding the Compound Interest with Periodic Deductions and learn the concept behind them.
Example Questions on Compound Interest with Periodic Deductions
1. Jasmine borrows $ 10,000 at a compound interest rate of 4% per annum. If she repays $ 2,000 at the end of each year, find the sum outstanding at the end of the second year?
Solution:
From the Given Data
Principal = $ 10, 000
Interest Rate = 4% Per Annum
Time = 1 Year
Interest = PTR/100
= 10,000*1*4/100
= $400
Amount of the loan after 1 year = Principal + Interest
= $10,000 + $400
= $10, 400
Jasmine Repays $2,000 after the first year
Therefore, New Principal for the 2nd year = $10, 400 – $2,000
= $8,400
Thus for 2nd Year Principal = $8, 400
Interest = 4%
Time = 1 Year
Interest = PTR/100
= 8,400*1*4/100
= $336
Amount after 2nd Year = Principal + Interest
= $8400+$336
= $8736
Therefore, Jasmine needs to pay an outstanding amount of $8736 dollars by the end of the 2nd Year.
2. David invests $ 10,000 at the beginning of every year in a bank and earns 5 % annual interest, compounded at the end of the year. What will be his balance in the bank at the end of two years?
Solution:
From the Given Data
Principal = $10, 000
Rate of Interest = 5%
Time = 1 Year
Interest = PTR/100
= 10,000*1*5/100
= $500
Therefore Amount after 1 Year = Principal + Interest
= $10,000+$500
= $10, 500
David deposits 10,000 at the beginning of the second year
New Principal becomes = $10, 500+ $10, 000
= $20, 500
Thus, for the 2nd Year
Principal = $20, 500
Interest Rate = 5%
Time = 1 Year
Interest = PTR/100
= $20, 500*1*5/100
= $1025
Amount after the 2nd Year = Principal + Interest
= $20, 500 + $1025
= $21, 525
Therefore, David will have $21, 525 in the bank after the end of 2 Years.
3. John lent $ 5,000 at a compound interest rate of 10% per annum. If he repays $ 500 at the end of the first year and $ 1,000 at the end of the second year, find his outstanding loan at the beginning of the third year?
Solution:
From the Given Data
Principal = $ 5,000
Interest rate = 10%
Time = 1 Year
Interest = PTR/100
= 5000*1*10/100
= $500
Amount after 1 year = Principal + Interest
= $5000+$500
= $5500
John repays $500 at the end of first year thus new principal = $5500 – $500
= $5000
Thus, For 2nd Year
New Principal = $5000
Time = 1 Year
Interest Rate = 10%
Interest = PTR/100
= $5000*1*10/100
= $500
Amount after 2nd Year = Principal + Interest
= $5,000+$500
= $5500
John repays $1000 after the end of 2nd year
Thus for third year New Principal = $5500 – $1000
= $4500
Therefore the outstanding loan at the beginning of the third year is $4500.
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