Find the amount of compound interest earned in an account that opens with $23,000, earns 3.9% interest compounded daily, and is held for 15 years. Assume 360 days in a year. (Round your answer to the nearest cent.)
i=.039/360=.000108333
n=15*360=5400
Amount=2300(1.000108333)^5400
=30153.83
Interest earned=30153.83-23000=$7,153.83
To find the compound interest earned, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan
P = the principal investment amount (the initial deposit or loan amount)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years the money is invested or borrowed for
In this case:
P = $23,000
r = 3.9% = 0.039 (as a decimal)
n = 365 (since it is compounded daily)
t = 15
Plugging in the values into the formula, we get:
A = 23000(1 + 0.039/365)^(365*15)
Now, let's calculate it step by step.
Step 1: Calculate the fraction inside the parentheses:
0.039/365 = 0.000106
Step 2: Add 1 to the fraction:
1 + 0.000106 = 1.000106
Step 3: Calculate the exponent:
365 * 15 = 5,475
Step 4: Raise the base to the exponent:
(1.000106)^5475 = 1.65490389147
Step 5: Multiply the result by the principal investment:
23000 * 1.65490389147 = 38043.55
Therefore, the future value (A) of the investment is $38,043.55.
To find the compound interest earned, subtract the principal investment from the future value:
Interest = A - P
Interest = 38043.55 - 23000 = $15,043.55
Hence, the compound interest earned in the account is approximately $15,043.55.