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CanadaON
Grade 11

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 $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}$173 $=$= $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 dollar.

Outcomes

11U.C.3.3

Solve problems, using a scientific calculator, that involve the calculation of the amount, A (also referred to as future value, FV), the principal, P (also referred to as present value, PV), or the interest rate per compounding period, i, using the compound interest formula in the form A = P(1 + i)^n [or FV = PV(1 + i)^n]

11U.C.3.4

Determine, through investigation using technology, the number of compounding periods, n, using the compound interest formula in the form A = P(1 + i)^n [or FV = PV(1 + i)^n ]; describe strategies

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