Measurement of interest

2 free worked examples

Solved in full, free to everyone, and never rotated. Read these before deciding whether the rest of the drill is worth paying for.

1. Exam FMMeasurement of interestCore

   An account earns an effective annual discount rate of 6%. Find the equivalent effective annual interest rate.

   1. A$5.6604\%$
   2. B$6.0000\%$
   3. C$6.3830\%$
   4. D$6.6000\%$
   5. E$12.7660\%$

   Solution

   1. The relationship between the two rates is $d=\frac{i}{1+i}$, which rearranges to $i=\frac{d}{1-d}$.
   2. $i=\frac{0.06}{1-0.06}=\frac{0.06}{0.94}$.
   3. $=0.063830$, or 6.3830%.
   4. The interest rate must EXCEED the discount rate, because discount is interest paid in advance - a useful check on the direction of the algebra.

   Trap. Computing d(1+d) = 6.36% or treating the two rates as equal.

2. Exam FMMeasurement of interestExam level

   At what effective annual rate does money double in 12 years?

   1. A$5.9463\%$
   2. B$6.0000\%$
   3. C$6.1163\%$
   4. D$8.3333\%$
   5. E$12.0000\%$

   Solution

   1. Solve $(1+i{)}^{12}=2$.
   2. $1+i=2^{1/12}=1.059463$.
   3. $i=5.9463\%$.
   4. The 'rule of 72' estimate $72/12=6\%$ is close, which is exactly why that approximation survives - but it is an approximation.
   5. The rule is most accurate near 8%; it drifts noticeably at very low or very high rates.

   Trap. Using the rule of 72 as though it were exact.