Finding missing value of time in compounnd interest

Question

In what time will Rs 64000 amount to Rs 68921 at 10% per annum, interest being compounded yearly?

Answer 1

A = p(+r/n)^nt

A = future amount = 68921

p = principal investment = 64000

r = interest rate as decimal = 0.1

n = # times compounded per year = 1

t = time in years

 

68921 = 64000(1+.1/1)^1(t)

68921 = 64000(1.1)^t

68921/64000 = 1.1^t

Take log of both sides

 

log (68921/64000) = log(1.1^t)

log (68921/64000) = t(log 1.1)

 

t = [log(68921/64000)]/(log 1.1)

 

Now punch this into calculator to determine

the value of t.

t = 0.777229 years

 

t = 9.3 months

Answer 2

A = p(1 + r)^t

68921 = 64000(1 + 0.10)^t

1.07689 ≈ 1.1^t

ln 1.07689 ≈ (t)(ln 1.1)

 

Can you calculate t?