Final answer:
To compute interest earned on an investment of $49,060 at 4.93% APR compounded daily for 218 days, the formula for compound interest is applied. The future value is approximately $50,125.90, and thus the total interest earned is approximately $1,065.90, rounded to the nearest cent.
Step-by-step explanation:
To calculate the total interest earned on an account after 218 days when $49,060 is invested at an annual percentage rate (APR) of 4.93%, compounded daily, the formula for compound interest is used:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount ($49,060 in this case)
r = the annual interest rate (decimal) (0.0493 for 4.93%)
n = the number of times that interest is compounded per year (365 for daily)
t = the time the money is invested or borrowed for, in years (218/365 for 218 days)
First, convert the APY to a daily rate and the time period to years:
daily rate (r/n) = 0.0493/365 = 0.0001350685
time in years (t) = 218/365 = 0.59726027397
Then, plug the values into the formula to find A:
A = $49,060(1 + 0.0001350685)^(365*0.59726027397)
Using a calculator, you find:
A ≈ $49,060(1.0001350685)^218
A ≈ $50,125.90 (rounded to the nearest cent)
The total interest earned is then:
Total Interest = A - P
Total Interest ≈ $50,125.90 - $49,060
Total Interest ≈ $1,065.90
The total interest earned on the account after 218 days is approximately $1,065.90, rounded to the nearest cent.