Question

In what time will rs.1000 amounts to rs.1331 at 20% per annum, compounded half yearly?

Answer 1

Compound interest accumulation factor :

P × (1 + i)ⁿ

P = amount deposited = 1000

i = interest rate = 20/2 = 10 — compounded semiannually

n = Time

Accumulated amount = 1331

Doing substitution :

1331 = 1000 × (1.10)ⁿ

1331/1000 = (1.10)ⁿ

1.331 = (1.10)ⁿ

Log 1.331 = n log 1.10

0.124178 = 0.041393n

n = 0.124178/0.041393 = 2.999975

= 3 periods

3/2 = 1.5 years

This is because it is compounded semiannually