find both the exact and ordinary interest on $32,000 at 8 1/4% for 106 days. then find the amount by which…

find both the exact and ordinary interest on $32,000 at 8 1/4% for 106 days. then find the amount by which the ordinary interest is larger. the exact interest on $32,000 at 8 1/4% for 106 days is $ (round to the nearest cent.) the ordinary interest on $32,000 at 8 1/4% for 106 days is $ (round to the nearest cent.)

find both the exact and ordinary interest on $32,000 at 8 1/4% for 106 days. then find the amount by which the ordinary interest is larger. the exact interest on $32,000 at 8 1/4% for 106 days is $ (round to the nearest cent.) the ordinary interest on $32,000 at 8 1/4% for 106 days is $ (round to the nearest cent.)

Answer

Explanation:

Step1: Convert the interest - rate to a decimal

The interest rate $r = 8\frac{1}{4}%=\frac{33}{4}% = 0.0825$.

Step2: Calculate the exact - interest

The formula for exact interest is $I = Prt$, where $P$ is the principal amount, $r$ is the annual interest rate, and $t$ is the time in years. For exact - time, $t=\frac{106}{365}$ (since there are 365 days in a non - leap year). Given $P = 32000$, then $I_{exact}=Prt=32000\times0.0825\times\frac{106}{365}$. [ \begin{align*} I_{exact}&=32000\times0.0825\times\frac{106}{365}\ &=32000\times0.0825\times0.290411\ &=32000\times0.023869\ & = 763.81 \end{align*} ]

Step3: Calculate the ordinary interest

The formula for ordinary interest is $I = Prt$, where for ordinary time, $t=\frac{106}{360}$ (since in ordinary interest calculations, we assume 360 days in a year). Given $P = 32000$ and $r = 0.0825$, then $I_{ordinary}=Prt=32000\times0.0825\times\frac{106}{360}$. [ \begin{align*} I_{ordinary}&=32000\times0.0825\times\frac{106}{360}\ &=32000\times0.0825\times0.294444\ &=32000\times0.024291\ &=777.31 \end{align*} ]

Answer:

The exact interest on $$32000$ at $8\frac{1}{4}%$ for 106 days is $$763.81$. The ordinary interest on $$32000$ at $8\frac{1}{4}%$ for 106 days is $$777.31$.