Investment FV Help 1

Rounded to the nearest quarter year, how long will it take an investment to quadruple if it earns 8% compounded semi-annually?

Any help would be greatly appreciated with calculations.

Thanks

This is very simple and easy problem to solve. He is basically asking: How long would it take for $1 to become $4 @8% S.A.

The first thing you should do is to convert 8% from S.A. compound to quarterly compound, which comes to 7.92% comp. quarterly. Then you would solve for n, or number of periods. If you do it right, you should get: 70.69 quarters, or rounded to the nearest quarter=71 quarters. or 70.69/4=17 years and 3 quarters(rounded to neatest quarter).

The formula you use is the same PV formula that you know. The only difficulty you might have is solving for n. You have to use Logs to do that.

4A = A( 1 + .08/2)^(2n)       divide both sides by A

4 = ( 1 + .08/2)^(2n)           take the log of both sides

log [4]   =  log (1.04)^(2n)     and we can wrtie

log [4]  =  (2n) log (1.04)      divide both sides by 2log(1.04)

log [4]  / [2log(1.04)]  = n   =   about 17.67 years  ≈  17 + 2/3   years