City Bank pays a simple interest rate of 3% per year, meaning that each year the balance increases by 3% of the initial deposit. National Bank pays an compound interest rate of 2.6% per year, compounded monthly, meaning that each month the balance increases by one twelfth of 2.6% of the previous month's balance.
National Bank, on the other hand, pays a lower interest rate, but compounds the interest monthly. This means that the account balance grows by \)\frac{2.6}{12}\%\( each month. Accordingly, after 10 years (120 months), the National Bank account balance is\begin{equation} \)10,000\left(1 + \frac{.026}{12}\right)^{120}\approx\(12,965.65. \end{equation} So City Bank provides the larger balance at the end of 10 years. However, similar computations show that the City Bank balance after 15 years is $14,500 while the National Bank balance is about \)14,763.57. Thus National Bank provides the larger balance after 15 years.
Length of investment | City Bank Balance | National Bank Balance |
---|---|---|
One Year (12 months) | $10,300.00 | $10,263.12 |
Two Year | $10,600.00 | $10,533.16 |
Three Year | $10,900.00 | $10,810.31 |
Four Year | $11,200.00 | $11,094.75 |
Five Year | $11,500.00 | $11,386.68 |
Six Year | $11,800.00 | $11,686.29 |
Seven Year | $12,100.00 | $11,993.78 |
Eight Year | $12,400.00 | $12,309.36 |
Nine Year | $12,700.00 | $12,633.25 |
Ten Year | $13,000.00 | $12,965.65 |
Eleven Year | $13,300.00 | $13,306.81 |
Twelve Year | $13,600.00 | $13,656.94 |
Thirteen Year | $13,900.00 | $14,016.28 |
Fourteen Year | $14,200.00 | $14,385.08 |
Fifteen Year | $14,500.00 | $14,763.58 |
Commentary
While somewhat realistic interest rates are presented in the task, the schemes for calculating interest earned as detailed in the problem statement are not representative of standard banking practices where interest is normally compounded on a daily basis.