Question

How long will it take a sum of money to double if interest is at 11% compounded semiannually?

Answer 1

Rate = 11% (semi-annual compounding),

Converting Rate into effective rate = r = (1+R/2)^2-1 = (1+11%/2)^2-1 = 11.3025%

Assuming invested amount = PV = $ 100

Expected amount is double of invested amount = FV = $ 200

Time = Tenor in years = t = ?

Formula of Present Value or PV:

PV = FV / (1+r)^t

100 = 200/(1+11.3025%)^t

100 = 200 / (1.113025)^t

(1.113025)^t = 200/100

(1.113025)^t = 2

Take natural log at both the sides;

t x ln(1.113025) = ln(2)

t x 0.107081534 = 0.693147181 [See note below]

t = 0.693147181 / 0.107081534

t = 6.473078556

t = ~ 6.47 years

Note: Value for ln(1.113025) = 0.107081534 and ln(2) = 0.693147181