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.
At what annual compound interest rate, $r$r, must Joanne invest $\$220$$220 if she wishes to triple her money in $17$17 years? Give your answer as a percentage correct to two decimal places.
Think: How much is triple the principal?
Do:
$220\times3$220×3 | $=$= | $\$660$$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.) |
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 dollar.