Interest & Annuity

1. Interest & Annuity
Suraj More – 7709685533
04/05/2018 Suraj - 7709685533 1

2. Interest and Annuity
Simple Interest
𝑆𝐼 =
𝑃 𝑥 𝑁 𝑥 𝑅
100
𝑖 =
𝑅
100
𝑆𝐼 = 𝑃 𝑥 𝑁 𝑥 𝑖
04/05/2018 Suraj - 7709685533 2

3. Illustration 1
1. Calculate Simple Interest on ₹ 20,000 for 3⅟2 years at 6 %
Rate of Interest per annum
Ans :4200
04/05/2018 Suraj - 7709685533 3

4. Illustration 2
• In How many years a sum of ₹50,000 will amount to ₹60,000 at
10% simple interest
Ans : N= 2 years
04/05/2018 Suraj - 7709685533 4

5. Illustration 3
• Simple interest on a certain for 4 years at 7 % is more than simple
interest on the same sum for 2.5 years at the same rate by rupees 840
find the principle amount
04/05/2018 Suraj - 7709685533 5

6. Illustration 4
• A simple Interest of 3240 is received after 3 years on a certain
principal at the rate of 9 % per annum . How much simple interest will
be obtained after 5 and half years from the same principal at the rate
of 7 % p.a.
04/05/2018 Suraj - 7709685533 6

7. Illustration 5
• Abhay borrowed ₹ 50,000 partly at 8 % p.a. and the remaining at 9 %
p.a. after 2
1
2
years , he returned the total amount with a total
simple interest of ₹ 10500 find the amounts he borrowed at each of
these rates .
04/05/2018 Suraj - 7709685533 7

8. Illustration 6
• Amit deposited ₹ 25000 in a co operative bank with simple interest
He withdrew ₹ 15000 ,from that amount and the interest as well , after
3 years . Again thereafter , he withdrew the remaining amount and the
interest accrued till that time , after 2 years . In all he received ₹ 7600
as total simple interest . Find the rate of interest p.a.
04/05/2018 Suraj - 7709685533 8

9. Illustration 7
• Anita and amisha borrowed ₹ 8,000 and 15,000 respectively at the
same rate of simple interest . After 3 years Anita repayed the loan by
giving ₹ 10,160 . How much amount should amisha pay after 4 and
half years , to pay off the loan , including simple interest
04/05/2018 Suraj - 7709685533 9

10. Compound Interest
• 𝐴 = 𝑃 1 +
𝑅
100
𝑛
• 𝐴 = 𝑃 1 + 𝑖 𝑛
• 𝐶𝐼 = 𝑝 1 + 𝑖 𝑛 − 1
• 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑓𝑜𝑟 𝑛 𝑡ℎ 𝑃𝑒𝑟𝑖𝑜𝑑 = 𝑃 1 + 𝑖 𝑛−1
(i)
• Formula can also be used for Depreciation as
• 𝐷𝑉 = 𝑝 1 − 𝑖 𝑛
04/05/2018 Suraj - 7709685533 10

11. Annuity
• We open a recurring deposit in a bank by paying a fixed Deposit
Every month after completion of specified date , you get a refund
Annuity - The series of payment made as successive intervals of time
is called an Annuity
Usually all the payments of an annuity are identical , which is called
Level or Uniform Annuity
04/05/2018 Suraj - 7709685533 11

12. Terms in Annuity
1. Immediate Annuity : if the annuities are paid at the end of each period ,
it is known as an Immediate Annuity
2. Annuity Due : If payments are paid at the beginning of each period
, It is called an Annuity Due
3. Annuity certain : If the total number of time periods is fixed , It is known as
Annuity Certain
4. Life Annuity : If the payments are to be made as long as a person is alive
It is called as life Annuity
04/05/2018 Suraj - 7709685533 12

13. Terms in Annuity
5. Contingent Annuity : An Annuity with Number of payments
depending on happening of an event is a contingent Annuity while
An annuity supposed to go on perpetually or endlessly is a Perpetual
Annuity or a Perpetuity
We will only Study Annuity certain and Immediate
04/05/2018 Suraj - 7709685533 13

14. Accumulated value ( Immediate Annuity )
• Here the payments are made at the end of period and we have to find
out the final accumulated value after n time Periods
• Let each annuity be of ₹ C , rate of Compound interest per unit per
annum be i
𝐴𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒 = 𝐶 𝑥 [{ 1 + 𝑖 𝑛
−1}/𝑖]
It represents Immediate Annuity
04/05/2018 Suraj - 7709685533 14

15. Illustration 31
• What is accumulated value after 4 years of an immediate annuity of
₹ 8000 p.a. The rate of interest being 8% P.a. ?
04/05/2018 Suraj - 7709685533 15

16. Illustration 33
• Find the amount at the end of 1 year of an annuity of 4000 payable at
each quarter , with rate of interest 12 % p.a.
04/05/2018 Suraj - 7709685533 16

17. Illustration 34
• Jiya deposited 2000 at the end of each year , for 2 years in a company
and received 4200 as the accumulated value . Find rate of compound
interest .
04/05/2018 Suraj - 7709685533 17

18. Illustration
• Sanjay invested 1000 at the end of every month for 4 years at 12 %
p.a Compound interest . Find the amount he will receive at the end
of the period .
04/05/2018 Suraj - 7709685533 18

19. Illustration 36
• Diana deposists 1650 at the end of each quarter for
3
1
2
𝑦𝑒𝑎𝑟𝑠 𝑎𝑡 9 % 𝑃. 𝑎. 𝐶𝑜𝑚𝑝𝑜𝑢𝑛𝑑 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 . 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑎𝑚𝑜𝑢𝑛𝑡 𝑠ℎ𝑒
will receive at the end of the period
04/05/2018 Suraj - 7709685533 19

20. Illustaration 37
• Manisha deposits 500 with 12 % compound interest for 3 years . Find
the Final Amount if
a. Payment is at end of each month
b. Payment is at the end of each quarter
04/05/2018 Suraj - 7709685533 20

21. Effective rate of Interest
• Effective Rate = 1 +
𝑖
𝑚
𝑚
− 1
04/05/2018 Suraj - 7709685533 21

22. Present worth or Value of Annuity
• 𝑃. 𝑉. =
𝐶 𝑥 1+𝑖 𝑛−1
1+𝑖 𝑛 𝑥 𝑖
04/05/2018 Suraj - 7709685533 22