Question

if a man saves Rs. 1000 each year and invests at the end of the year at 5%
ts at the end of the year at 5% compound interest, how much will the
Imount be at the end of 15 years?
a) Rs. 21,478
(b)Rs. 21,578
(c) Rs. 22,578
(d) Rs. 22,478​

Answer 1

Answer:

The answer is (b) Rs.21,578

Step-by-step explanation:

You should consider this as a series of investments with compound interest. This is a set of 15 investments of Rs.1,000 each, at 5 per cent compound interest. However, each investment has a different time period. The investment exercise ends at the END of the 15th year.

At the end of the first year, Rs.1,000 is invested. This has a duration of 14 years. (Difference between end of 15th year and end of 1st year is 14 years)

Using the formula for compound interest, the final amount will be:

A = P*(1+R/100)^T

P=1000; R = 5; T = 14

Solving this, we get A = 1979.93

Similarly, we do the investments for the end of the second year, third year and so on up to the end of the 14th year.

At the end of the 15th year, an investment of Rs.1000 is made. However, this investment bears no interest as it is present for "zero" time.

The following table gives the calculations:

P is Principal; T is number of years; A = final amount. The first column shows the "end of the year".

P          T  A

1 1000 14 1,979.93

2 1000 13 1,885.65

3 1000 12 1,795.86

4 1000 11 1,710.34

5 1000 10 1,628.89

6 1000 9 1,551.33

7 1000 8 1,477.46

8 1000 7 1,407.10

9 1000 6 1,340.10

10 1000 5 1,276.28

11 1000 4 1,215.51

12 1000 3 1,157.63

13 1000 2 1,102.50

14 1000 1 1,050.00

15 1000 0 1,000.00

Total   21,578.56