Question

If a zero-coupon bond has a stated annual interest rate of 18%, compounded continuously, how many years will it take to double the value of the bond? (Assume that the bond will double in value before it matures)

Select one: a. 3.9 b. 4.19 c. 3.29 d. 3.85 e. 5.2

Answer 1

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

A= P ( 1+ 18/100) ^ n

Let P = $ x

Hence, A= $ 2x

Hence, 2x = x*(1+18/100) ^n

or 2 = (1.18) ^ n

Taking log on both sides we get,

log 2 = n log (1.18)

Hence, n = Log 2 / log (1.18)

or n = 4.19 years

Hence the correct answer is b. 4.19