Answer:
He earns $0.24 in interest after 1 day.
Step-by-step explanation:
Compound interest:
![A(t)=P(1+\frac{r}{n})^{n\ast t}](https://tex.z-dn.net/?f=A%28t%29%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bn%5Cast%20t%7D)
In which:
P is the principal, the amount of the initial deposit.
r is the yearly interest rate, as a decimal.
n is the number of compoundings during a year.
t is the number of years.
In this question:
Deposit of $1,750, so P = 1750.
Interest rate of 5%, so r = 0.05.
Compounded daily. A year has 365 days, so n = 365.
After 1 day. 1 day is 1/365 of an year, so t = 1/365.
The amount he will have after one day will be:
![A=1750(1+\frac{0.05}{365})^{\frac{1}{365}\ast365}=1750(1+\frac{0.05}{365})=1750.24](https://tex.z-dn.net/?f=A%3D1750%281%2B%5Cfrac%7B0.05%7D%7B365%7D%29%5E%7B%5Cfrac%7B1%7D%7B365%7D%5Cast365%7D%3D1750%281%2B%5Cfrac%7B0.05%7D%7B365%7D%29%3D1750.24)
The interest earned will be:
Amount after 1 day subtracted by the deposit.
Deposit of $1,750.
After 1 day, he will have $1,750.24.
1750.24 - 1750 = 0.24
He earns $0.24 in interest after 1 day.