Compound Interest with Periodic Deductions

We will learn how to calculate the compound interest with periodic deductions or additions to the amount.

Solved examples on compound interest with periodic deductions:

1. Ron borrows $ 10,000 at a compound interest rate of 8% per annum. If he repays $ 2000 at the end of each year, find the sum outstanding at the end of the third year.

Solution:

For the first year:

Principal = $ 10,000

Rate = 8 %

Time = 1 year

Therefore, interest = $\(\frac{P × R × T}{100}\)

                          = $\(\frac{10000 × 8 × 1}{100}\)

                          = $\(\frac{80000}{100}\)

                          = $ 800

Therefore, the amount of loan after 1 year = Principal + Interest

                                                          = $ 10,000 + $ 800

                                                          = $ 10,800

Ron pays back $ 2,000 at the end of the first year.

So, the new principal at the beginning of the second year = $ 10,800 - $ 2,000                                                                                = $ 8,800

Therefore, for the second year:

Principal = $ 8,800

Rate = 8 %

Time = 1 year

Therefore, interest = $\(\frac{P × R × T}{100}\)

                          = $\(\frac{8,800 × 8 × 1}{100}\)

                          = $\(\frac{70400}{100}\)

                          = $ 704

Therefore, the amount of loan after 2 year = Principal + Interest

                                                          = $ 8,800 + $ 704

                                                          = $ 9504

Ron pays back $ 2,000 at the end of the second year.

So, the new principal at the beginning of the third year = $ 9504 - $ 2,000

                                                                           = $ 7504

Therefore, for the third year:

Principal = $ 7504

Rate = 8 %

Time = 1 year

Therefore, interest = $\(\frac{P × R × T}{100}\)

                          = $\(\frac{7504 × 8 × 1}{100}\)

                          = $\(\frac{60032}{100}\)

                          = $ 600.32

Therefore, the amount of loan (outstanding sum) after 3 year = Principal + Interest

                                                                                   = $ 7504 + $ 600.32

                                                                                   = $ 8104.32


2. Davis invests $ 20,000 at the beginning of every year in a bank and earns 10 % annual interest, compounded at the end of the year. What will be his balance in the bank at the end of three years.

Solution:

For the first year:

Principal = $ 20,000

Rate = 10 %

Time = 1 year

Therefore, interest = $\(\frac{P × R × T}{100}\)

                          = $\(\frac{20000 × 10 × 1}{100}\)

                          = $\(\frac{200000}{100}\)

                          = $ 2000

Therefore, the amount at the end of the 1 year = Principal + Interest

                                                                 = $ 20,000 + $ 2000

                                                                 = $ 22,000

Davis deposits $ 20,000 at the beginning of the second year.

So, the new principal for the second year = $ 22,000 + $ 20,000

                                                        = $ 42,000

Therefore, for the second year:

Principal = $ 42,000

Rate = 10 %

Time = 1 year

Therefore, interest = $\(\frac{P × R × T}{100}\)

                          = $\(\frac{42000 × 10 × 1}{100}\)

                          = $\(\frac{420000}{100}\)

                          = $ 4,200

Therefore, the amount at the end of the 2 year = Principal + Interest

                                                                = $ 42,000 + $ 4,200

                                                                = $ 46,200

Davis deposits $ 20,000 at the beginning of the third year.

So, the new principal for the third year = $ 46,200 + $ 20,000

                                                     = $ 66,200

Therefore, for the third year:

Principal = $ 66,200

Rate = 10 %

Time = 1 year

Therefore, interest = $\(\frac{P × R × T}{100}\)

                          = $\(\frac{66200 × 10 × 1}{100}\)

                          = $\(\frac{662000}{100}\)

                          = $ 6620

Therefore, the amount at the end of the 3 year = Principal + Interest

                                                                 = $ 66,200 + $ 6,620

                                                                 = $ 72,820

Therefore, the balance in the bank at the end of thee years will be $ 72,820.


From the above examples, we observe that how the principal does not remain same always; at the end of every phase, the principal changes. There is a direct relation between the principal and the compound interest or amount.

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Worksheet on Compound Interest




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