Example 5 of 7 · Finance: a loan repayment

AI HL · Mathematics

Sam borrows CHF 20 000 over 5 years, repaid monthly. The bank quotes 4% per year compounded monthly, rounded to the nearest whole percent. Find the maximum percentage error in the monthly repayment.

Smallest true value · 3.5%

TI-Nspire · Finance Solver
N60
I(%)3.5
PV20 000
Pmt−363.83
FV0
PpY12
CpY12
\[\begin{aligned}T_2&=363.83\\[6pt]\class{mjx-pe-s6}{\%\text{ error}}&\class{mjx-pe-s6}{{}=\left|\frac{368.33-363.83}{363.83}\right|\times100}\\[6pt]&\class{mjx-pe-s6}{{}=\class{mjx-pe-key}{\boldsymbol{1.24\%}}}\end{aligned}\]

Approximate value · 4%

TI-Nspire · Finance Solver
N60
I(%)4
PV20 000
Pmt−368.33
FV0
PpY12
CpY12
\[\begin{aligned}A&=368.33\\[6pt]\class{mjx-pe-s5}{\%\text{ error}}&\class{mjx-pe-s5}{{}=\left|\frac{A-T}{T}\right|\times100}\end{aligned}\]

Largest true value · 4.5%

TI-Nspire · Finance Solver
N60
I(%)4.5
PV20 000
Pmt−372.86
FV0
PpY12
CpY12
\[\begin{aligned}T_1&=372.86\\[6pt]\class{mjx-pe-s7}{\%\text{ error}}&\class{mjx-pe-s7}{{}=\left|\frac{368.33-372.86}{372.86}\right|\times100}\\[6pt]&\class{mjx-pe-s7}{{}=\class{mjx-pe-key}{\boldsymbol{1.21\%}}}\end{aligned}\]

Maximum percentage error = 1.24%. The rate could be out by 0.5 percentage points, yet the repayment is only out by about CHF 4.50 a month.