Question

a sum of rs 15625 amounts to rs 17576 at 8% per annum , compounded semi annually.find the time

Answer 1

principal=15625
r=8%
amount=17576
amount=p(1+(r/100))^n             (where n is time)
amount=15625(1+(8/100))^n
17576=15625((100+8)/100)^n
17576/15625=(108/100)^n

Answer 2

Let principal = $ P, rate = R % per annum and time = n years.

Then, the amount A is given by the formula
A = P (1 + R/100)n
Therefore, compound interest = (amount) - (principal).
1. Find the amount of $ 8000 for 3 years, compounded annually at 5% per annum. Also, find the compound interest.
Solution:

Here, P = $ 8000, R = 5 % per annum and n = 3 years.

Using the formula A = $ P(1 + R/ 100)n

amount after 3 years = $ {8000 × (1 + 5/100)3}

= $ (8000 × 21/20 × 21/20 × 21/20)

= $ 9261.

Thus, amount after 3 years = $ 9261.

And, compound interest = $ (9261 - 8000)

Therefore, compound interest = $ 1261.

2. Find the compound interest on $ 6400 for 2 years, compounded annually at 71/2 % per annum.
Solution:

Here, P = $ 6400, R % p. a. and n = 2 years.

Using the formula A = P (1 + R/100)n

Amount after 2 years = [6400 × {1 + 15/(2 × 100)}2]

= $ (6400 × 43/40 × 43/40)

=$ 7396.

Thus, amount = $ 7396

and compound interest = $ (7396 - 6400)

Therefore, compound interest = $ 996.




When interest is compounded annually but time is a fraction
For example suppose time is 23/5 years then,

Amount = P × (1 + R/100)2 × [1 + (3/5 × R)/100]

1. Find the compound interest on $ 31250 at 8 % per annum for 2 years. Solution Amount after 23/4 years
Solution:

Amount after 23/4 years

= $ [31250 × (1 + 8/100)2 × (1 + (3/4 × 8)/100)]

= ${31250 × (27/25)2 × (53/50)}

= $ (31250 × 27/25 × 27/25 × 53/50)

= $ 38637.

Therefore, Amount = $ 38637,

Hence, compound interest = $ (38637 - 31250) = $ 7387.