if a principal, P, is invested at r% interest compounded annually then its future value, S, after n years is given by
$\large S=P(1+ \frac{r}{100})^n $
Use this formula to show that if an interest rate of r% is compounded k times a year, then after t years
$\large S=P(1+ \frac{r}{100k})^kt $

Question

if a principal, P, is invested at r% interest compounded annually then its future value, S, after n years is given by
$\large S=P(1+ \frac{r}{100})^n $
Use this formula to show that if an interest rate of r% is compounded k times a year, then after t years
$\large S=P(1+ \frac{r}{100k})^kt $

sasogeek · Answer

Use this formula to show that if an interest rate of r% is compounded k times a year, then after t years $\large S=P(1+\frac{r}{100k})^{kt} $

sasogeek · Answer

i made a mistake with the "t" in the initial question, corrected above :)

across · Answer

In the formula$$S=P\left(1+\frac{r}{100k}\right)^{kt},$$"compounded anually" translates to $k=1$, and if you let $n=t$, then you are left with$$S=P\left(1+\frac{r}{100}\right)^n.$$

across · Answer

That's a hint, by the way.

sasogeek · Answer

yeah i noticed :) thanks x