# Compound Interest - Finding other values

Lesson

We've already learnt about the compound interest formula but we have been using it mostly to find the total amount, $A$A. However we can also used this formula to find the principal amount, $P$P, the interest rate, $r$r, or the time duration, $n$n.

Remember the compound interest formula is:

$A=P\left(1+r\right)^n$A=P(1+r)n

If we want to find an unknown other than $A$A, we substitute in the values we know, then just rearrange the equation to change the subject of the formula, then solve the equation as usual.

#### Worked example

At what annual compound interest rate, $r$r, must Joanne invest $\$220$$220 if she wishes to triple her money in 1717 years? Give your answer as a percentage correct to two decimal places. Think: How much is triple the principal? Do:  220\times3220×3 == \660$$660 $A$A $=$= $P\left(1+r\right)^n$P(1+r)n $660$660 $=$= $220\times\left(1+r\right)^{17}$220×(1+r)17 (divide both sides by $220$220) $3$3 $=$= $\left(1+r\right)^{17}$(1+r)17 $\sqrt[17]{3}$17√3 $=$= $1+r$1+r (subtract $1$1 from both sides) $r$r $=$= $0.0667$0.0667 ... $r$r $=$= $6.68%$6.68% (to $2$2 d.p.)

#### Practice question

Find the amount, $P$P, that would need to be invested at $6%$6% p.a. compounded monthly to accumulate $£5600$£5600 in $9$9 years. Give your answer to the nearest pound.