Final answer:
To calculate the total interest earned on a certificate of deposit with daily interest compounding, we use the compound interest formula. Vince's CD has an initial deposit of $4,635, an effective annual rate of 4.73%, and it matures in 18 months.
Step-by-step explanation:
The student has asked how much total interest will be earned on an 18-month certificate of deposit (CD) with an initial deposit of $4,635 and an effective rate of interest of 4.73% where interest compounds daily.
To calculate the interest earned, we use the formula for compound interest: A = P(1 + r/n)^(nt), where:
- P is the principal amount ($4,635)
- r is the annual interest rate (4.73% or 0.0473 as a decimal)
- n is the number of times interest is compounded per year (daily compounding so n=365)
- t is the time the money is invested for in years (18 months or 1.5 years)
We calculate the amount in the account (A) after 18 months and then subtract the initial deposit (P) to find the total interest earned.