I need to compare the interest rate between 3 banks.
“H bank” offers 2.5% interest rate p.a. and will pay to my account monthly. “G bank” offers 2.0% interest rate p.a. and will pay to my account daily. “R bank” offers 4.0% interest rate p.a. and will pay to my account daily.
Are there big differences?
Effective Annual Yield#
To compare the interest rates effectively, we need to calculate the effective annual yield (EAY) for each bank, as the compounding frequency (monthly vs. daily) impacts the actual return. The formula for EAY is:
% EAY (KaTeX block notation) $$ EAY = \left(1 + \frac{r}{n}\right)^n - 1 $$
where (r) is the nominal annual interest rate, and (n) is the number of compounding periods per year (12 for monthly, 365 for daily).
Calculations#
H Bank: 2.5% p.a., compounded monthly ( r = 0.025 ), ( n = 12 ) $$ EAY = \left(1 + \frac{0.025}{12}\right)^{12} - 1 \approx 0.025305 \text{ or } 2.5305% $$
G Bank: 2.0% p.a., compounded daily ( r = 0.02 ), ( n = 365 ) $$ EAY = \left(1 + \frac{0.02}{365}\right)^{365} - 1 \approx 0.020201 \text{ or } 2.0201% $$
R Bank: 4.0% p.a., compounded daily ( r = 0.04 ), ( n = 365 ) $$ EAY = \left(1 + \frac{0.04}{365}\right)^{365} - 1 \approx 0.040811 \text{ or } 4.0811% $$
Comparison#
- H Bank: 2.5305% EAY
- G Bank: 2.0201% EAY
- R Bank: 4.0811% EAY
Differences#
- R Bank offers the highest effective yield (4.0811%), significantly outperforming both H Bank (2.5305%) and G Bank (2.0201%).
- The difference between R Bank and H Bank is ~1.55% p.a., and between R Bank and G Bank is ~2.06% p.a.
- H Bank outperforms G Bank by ~0.51% p.a., despite G Bank’s daily compounding, because H Bank’s nominal rate is higher.
- For a $10,000 deposit over one year:
- R Bank: ~$408.11 interest
- H Bank: ~$253.05 interest
- G Bank: ~$202.01 interest
- R Bank earns ~$155 more than H Bank and ~$206 more than G Bank annually.
Conclusion#
Yes, there are significant differences. R Bank provides the best return due to its higher nominal rate and daily compounding. H Bank is better than G Bank, but the gap between R Bank and the others is substantial.
EAY comparison:
