How many years will it take 1000 to grow to 1500 if ti is invested at 3% . A) compounded quarterly, B) compounded daily

Compunded quarterly:

1500=1000\left(1+\frac{.03}{4}\right)^{4t}

Solve for t:

\frac{3}{2}=(\frac{403}{400})^{4t}

ln(\frac{3}{2})=4tln(\frac{403}{400})

t=\frac{ln(\frac{3}{2})}{4ln(\frac{403}{400})}

For daily, use the same method, except use n=360.

I believe 360 is normally used for compounding daily instead of 365

EDIT: Oops, didn't know you posted before me galactus... :o


I learned the formula like this:

Money = Principal x (1+Rate)^t

Rearranging, it gives:

t = log (Money/Principal) / log (1+Rate)

t = log (1500/1000) / log (1+0.03) = 13.7 years (if rate is 3% yearly)

A scientific calculator is very handy if you cannot calculate this.

EDIT: Oops, didn't know you posted before me galactus... :o


Quite all right, U-Man. This formula is a good exercise in use of the log laws.

I like using fractions over decimals. That is why I converted everything to fractions. If for no other reason except for aesthetics.:D

One could run this through a calculator with a solver or in Excel.

It jives perfectly with my hand solution. A blind squirrel finds a nut once in a while.:)